Important Notes - JEE - Physics - Simple Harmonic MotionEdnexa
The document provides information about online courses on oscillatory motion and simple harmonic motion (S.H.M.) including live webinars, recorded lectures, online tests and solutions, notes, and career counseling. It then defines oscillatory motion and S.H.M., describing S.H.M. as periodic motion produced by a restoring force directly proportional to and opposite of the displacement. Several types and properties of S.H.M. are outlined, including the equations for displacement, velocity, acceleration, and differential equations of S.H.M. Examples and special cases are provided.
1) Simple harmonic motion describes any oscillatory motion where the restoring force is directly proportional to the displacement. It follows the differential equation d2x/dt2 = -ω2x, where ω is the angular frequency.
2) The position as a function of time for simple harmonic motion is given by x(t) = Acos(ωt + φ), which describes a simple sinusoidal oscillation.
3) When a damping force is present that is proportional to the velocity, the motion is described by damped harmonic motion. The amplitude decreases exponentially with time in underdamped systems.
1. Simple harmonic motion is motion influenced by a restoring force proportional to displacement from equilibrium. For a spring, F=-kx, and for a pendulum, F=mg sinθ.
2. The period T of a spring is the time for one complete oscillation, related to spring constant k and mass m by T=2π√(m/k). Frequency f is the number of oscillations per second, with f=1/T.
3. The displacement y of a spring over time t follows a sinusoidal pattern described by the equation y=A sin(2πft+θ0), where A is the amplitude
PHYSICS - Chapter 5: Oscillations Exercise SolutionPooja M
1. The document discusses linear simple harmonic motion (S.H.M.) and provides examples and derivations of key equations related to S.H.M. including expressions for velocity, acceleration, and period of oscillation for a simple pendulum and a magnet vibrating in a uniform magnetic field.
2. It is shown that S.H.M. is the projection of uniform circular motion along any diameter of the circle. Graphs of displacement, velocity, and acceleration versus phase angle are provided for a particle performing S.H.M. from the mean and extreme positions.
3. Key conclusions are that the restoring force in S.H.M. is directly proportional to displacement and acts in the
PHYSICS (CLASSS XII) - Chapter 5 : OscillationsPooja M
1. Oscillatory motion is a periodic motion that repeats itself after a definite time interval called the period. Linear simple harmonic motion (S.H.M.) is the linear periodic motion of a body where the restoring force is directly proportional to the displacement from the mean position.
2. The differential equation of S.H.M is the second derivative of displacement (x) plus the angular frequency (ω) squared times x equals zero. The expressions for displacement, velocity, and acceleration of a particle in S.H.M involve sinusoidal and cosine functions of angular frequency times time.
3. The amplitude is the maximum displacement, the period is the time for one oscillation, and the frequency is
The document links circular motion to simple harmonic motion (SHM) by using the motion of a ball rotating on a turntable to represent circular motion, and the shadow of a pendulum attached to the ball to represent SHM. It derives the equations for displacement, velocity, and acceleration of the pendulum's SHM from the ball's uniform circular motion. The displacement is described by a cosine function, the velocity is described by the square root of a quantity minus the displacement squared, and the acceleration is directly proportional to and opposite in direction from the displacement. All properties vary sinusoidally with time for SHM.
This chapter discusses simple harmonic motion (SHM). SHM is defined as periodic motion where the acceleration is directly proportional to and opposite of the displacement from equilibrium. The key equations of SHM are introduced, including the displacement equation x = A sin(ωt + φ) and equations for velocity, acceleration, kinetic energy, and potential energy using angular frequency ω. Examples of SHM include a simple pendulum and spring oscillations. Exercises are provided to apply the kinematic equations of SHM.
This document provides an overview of simple harmonic motion and pendulums. It includes:
- Objectives of understanding oscillations, deriving laws of oscillations, using Hooke's Law, and understanding simple harmonic motion.
- Experiments with a simple pendulum to determine factors affecting its period, including recording time for oscillations while varying length and mass.
- Theoretical analysis showing the period of a simple pendulum is proportional to the square root of its length.
- Deriving and solving the differential equation of motion for a simple pendulum using energy considerations.
- Examples of other oscillations that can be modeled using the derived simple harmonic motion equation.
Important Notes - JEE - Physics - Simple Harmonic MotionEdnexa
The document provides information about online courses on oscillatory motion and simple harmonic motion (S.H.M.) including live webinars, recorded lectures, online tests and solutions, notes, and career counseling. It then defines oscillatory motion and S.H.M., describing S.H.M. as periodic motion produced by a restoring force directly proportional to and opposite of the displacement. Several types and properties of S.H.M. are outlined, including the equations for displacement, velocity, acceleration, and differential equations of S.H.M. Examples and special cases are provided.
1) Simple harmonic motion describes any oscillatory motion where the restoring force is directly proportional to the displacement. It follows the differential equation d2x/dt2 = -ω2x, where ω is the angular frequency.
2) The position as a function of time for simple harmonic motion is given by x(t) = Acos(ωt + φ), which describes a simple sinusoidal oscillation.
3) When a damping force is present that is proportional to the velocity, the motion is described by damped harmonic motion. The amplitude decreases exponentially with time in underdamped systems.
1. Simple harmonic motion is motion influenced by a restoring force proportional to displacement from equilibrium. For a spring, F=-kx, and for a pendulum, F=mg sinθ.
2. The period T of a spring is the time for one complete oscillation, related to spring constant k and mass m by T=2π√(m/k). Frequency f is the number of oscillations per second, with f=1/T.
3. The displacement y of a spring over time t follows a sinusoidal pattern described by the equation y=A sin(2πft+θ0), where A is the amplitude
PHYSICS - Chapter 5: Oscillations Exercise SolutionPooja M
1. The document discusses linear simple harmonic motion (S.H.M.) and provides examples and derivations of key equations related to S.H.M. including expressions for velocity, acceleration, and period of oscillation for a simple pendulum and a magnet vibrating in a uniform magnetic field.
2. It is shown that S.H.M. is the projection of uniform circular motion along any diameter of the circle. Graphs of displacement, velocity, and acceleration versus phase angle are provided for a particle performing S.H.M. from the mean and extreme positions.
3. Key conclusions are that the restoring force in S.H.M. is directly proportional to displacement and acts in the
PHYSICS (CLASSS XII) - Chapter 5 : OscillationsPooja M
1. Oscillatory motion is a periodic motion that repeats itself after a definite time interval called the period. Linear simple harmonic motion (S.H.M.) is the linear periodic motion of a body where the restoring force is directly proportional to the displacement from the mean position.
2. The differential equation of S.H.M is the second derivative of displacement (x) plus the angular frequency (ω) squared times x equals zero. The expressions for displacement, velocity, and acceleration of a particle in S.H.M involve sinusoidal and cosine functions of angular frequency times time.
3. The amplitude is the maximum displacement, the period is the time for one oscillation, and the frequency is
The document links circular motion to simple harmonic motion (SHM) by using the motion of a ball rotating on a turntable to represent circular motion, and the shadow of a pendulum attached to the ball to represent SHM. It derives the equations for displacement, velocity, and acceleration of the pendulum's SHM from the ball's uniform circular motion. The displacement is described by a cosine function, the velocity is described by the square root of a quantity minus the displacement squared, and the acceleration is directly proportional to and opposite in direction from the displacement. All properties vary sinusoidally with time for SHM.
This chapter discusses simple harmonic motion (SHM). SHM is defined as periodic motion where the acceleration is directly proportional to and opposite of the displacement from equilibrium. The key equations of SHM are introduced, including the displacement equation x = A sin(ωt + φ) and equations for velocity, acceleration, kinetic energy, and potential energy using angular frequency ω. Examples of SHM include a simple pendulum and spring oscillations. Exercises are provided to apply the kinematic equations of SHM.
This document provides an overview of simple harmonic motion and pendulums. It includes:
- Objectives of understanding oscillations, deriving laws of oscillations, using Hooke's Law, and understanding simple harmonic motion.
- Experiments with a simple pendulum to determine factors affecting its period, including recording time for oscillations while varying length and mass.
- Theoretical analysis showing the period of a simple pendulum is proportional to the square root of its length.
- Deriving and solving the differential equation of motion for a simple pendulum using energy considerations.
- Examples of other oscillations that can be modeled using the derived simple harmonic motion equation.
The document discusses harmonic motion and traveling waves. It defines periodic and harmonic motion, and notes that harmonic motion can be described by a sinusoidal function. Hooke's law relating force and displacement in springs is introduced. Equations of motion for simple harmonic oscillators like masses on springs and pendulums are derived. The relationship between wavelength, frequency and propagation velocity is defined for traveling waves. Solutions to the wave equation for strings and their properties are also summarized.
This document discusses simple harmonic motion (SHM). SHM occurs when an object experiences a restoring force proportional to its displacement from equilibrium. This results in sinusoidal oscillations described by x(t) = Acos(ωt + φ), where A is amplitude, ω is angular frequency, and φ is the phase. SHM includes examples like a mass on a spring and a simple pendulum. The relationships between displacement, velocity, acceleration, period, frequency, and energy in SHM systems are explored.
The document discusses simple harmonic motion (SHM), where a particle moves back and forth such that its acceleration is directly proportional to its distance from a fixed point. SHM has the properties that the particle's velocity is zero at the amplitude of its oscillation, and it travels between the points of -a and +a on its axis. Examples are given of particles moving according to SHM equations, and exercises are provided to practice determining SHM, periods of motion, and maximum values.
Application of laplace wave equation in musicLuckshay Batra
This document discusses the application of the Laplace wave equation to music. The Laplace equation is a partial differential equation that can describe wave propagation phenomena. The document presents a problem involving the transverse vibrations of an elastic string that is stretched and fixed at both ends. The solution to this problem is the one-dimensional wave equation. The wave equation and its variants are important for understanding sound wave production and propagation in musical instruments, concert halls, and other spaces.
This document discusses the simple harmonic oscillator. It defines a simple harmonic oscillator as an oscillator that is neither driven nor damped, with motion that is periodic and sinusoidal with constant amplitude. The acceleration of a body in simple harmonic motion is directly proportional to and directed towards the displacement from the equilibrium position. General equations for displacement, velocity, and acceleration as a function of time and other variables are provided. Quantum mechanical treatment of the simple harmonic oscillator is also summarized. Examples of simple harmonic oscillators include a mass on a spring and a simple pendulum in small angle approximation.
The document discusses oscillations and simple harmonic motion. It defines periodic motion, oscillatory motion, and harmonic motion. Harmonic motion can be described using sine and cosine functions. Examples of oscillations include a swinging pendulum and vibrating springs. The period and frequency of oscillations are defined. For simple harmonic motion, the displacement is directly proportional to the displacement from equilibrium and opposite in sign. The velocity and acceleration functions for SHM are derived. For a mass-spring system, the restoring force is proportional to the displacement. The total mechanical energy of a simple harmonic oscillator remains constant over time as the kinetic and potential energy alternately increase and decrease during oscillation.
This document discusses oscillations and wave motion. It begins by introducing mechanical vibrations and simple harmonic motion. It then covers damped and driven oscillations, as well as different oscillating systems like springs, pendulums, and driven oscillations. The document goes on to discuss traveling waves, the wave equation, periodic waves on strings and in electromagnetic fields. It also covers waves in three dimensions, reflection, refraction, diffraction, and interference of waves. Key concepts covered include amplitude, frequency, period, angular frequency, energy of oscillating systems, and resonance.
1. This document contains solutions to problems from Chapter 1 of the textbook "The Physics of Vibrations and Waves".
2. It provides detailed calculations and explanations for problems related to simple harmonic motion, including determining restoring forces, stiffness, frequencies, and solving differential equations of motion.
3. Examples include a simple pendulum, a mass on a spring, and vibrations of strings, membranes, and gas columns.
The document discusses the wave equation and its application to modeling vibrating strings and wind instruments. It describes how the wave equation can be separated into independent equations for time and position using the assumption that displacement is the product of separate time and position functions. This separation leads to trigonometric solutions that satisfy the boundary conditions of strings fixed at both ends. The solutions represent standing waves with discrete frequencies determined by the length, tension, and density of the string. Similar methods apply to wind instruments with different boundary conditions.
This document discusses simple harmonic motion (SHM) and related concepts like angular velocity, restoring forces, displacement, velocity, acceleration, energy, resonance, and damping. It provides equations for angular velocity, SHM acceleration, displacement, velocity, energy, and the simple pendulum. Examples are given and questions provided for practice calculations involving these equations and concepts.
The document discusses key concepts from Einstein's special theory of relativity, including:
1) Frames of reference and the distinction between inertial and non-inertial frames. The laws of motion only hold in inertial frames.
2) The postulates of special relativity - that the laws of physics are the same in all inertial frames, and that the speed of light is constant.
3) Consequences of these postulates, including Lorentz transformations, length contraction, time dilation, and the relativity of simultaneity.
4) Experiments that motivated relativity, like the Michelson-Morley experiment, and equations like Lorentz transformations that were developed to be consistent with the postulates
This document discusses simple harmonic motion and elasticity. It begins by defining simple harmonic motion as back-and-forth motion caused by a restoring force proportional to displacement, with displacement centered around an equilibrium position. It then discusses Hooke's law, where the restoring force of an ideal spring is directly proportional to displacement. Several equations for simple harmonic motion are presented, including those relating displacement, velocity, acceleration, period, frequency, and amplitude. Examples are provided to illustrate these concepts for springs and pendulums undergoing simple harmonic motion.
(1) The document describes a theoretical physics problem involving a pendulum bob suspended from a rigid cylindrical rod. (2) It asks a series of questions about the motion of the pendulum bob and its velocity and acceleration at different points in its swing. (3) It also considers a variation where a heavier weight is attached below the pendulum, causing it to fall as the pendulum swings, and asks for the critical ratio of the weight's fall distance to the total string length needed for the pendulum to swing all the way around the rod.
The slides are designed for my guided study in MSc CUHK.
It is about the brief description on classical mechanics and quantum mechanics .
Some Slides I got from the slideshare clipboards for better illustration of the ideas in Physics. Thanks to slideshare, I make a milestone on presenting one of the prominent fields in modern physics.
The two waves would pass through each other and continue traveling in their original directions. At the point where they meet, both waves would be visible as their displacements add together through superposition. If a crest met a trough, they would undergo destructive interference and cancel each other out at the point where they meet.
This document defines key terms and equations related to simple harmonic motion (SHM). It discusses oscillating systems that vibrate back and forth around an equilibrium point, like a mass on a spring or pendulum. The key parameters of SHM systems are defined, including amplitude, wavelength, period, frequency, displacement, velocity, acceleration. Equations are presented that relate the displacement, velocity, acceleration as sinusoidal functions of time. The concepts of kinetic, potential and total energy are also explained for oscillating systems undergoing SHM.
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
CLASS XII - CHAPTER 5: OSCILLATION (PHYSICS - MAHARASHTRA STATE BOARD)Pooja M
This document provides information about oscillations and simple harmonic motion (SHM). It defines oscillation as periodic motion that repeats after a definite time interval. SHM is described as oscillatory motion where the restoring force is directly proportional to displacement from the equilibrium position. The key characteristics of SHM include:
- The differential equation relating displacement, velocity, and acceleration.
- Expressions for displacement, velocity, and acceleration as functions of time and constants.
- Definitions and calculations of important terms like amplitude, period, frequency, phase.
- Conditions required for motion to be considered SHM.
- Examples of SHM and calculations related to restoring force and period.
Text Book: An Introduction to Mechanics by Kleppner and Kolenkow
Chapter 1: Vectors and Kinematics
-Explain the concept of vectors.
-Explain the concepts of position, velocity and acceleration for different kinds of motion.
References:
Halliday, Resnick and Walker
Berkley Physics Volume-1
Physical Society the sentence but short speech on challenges of educational system in Bangladesh studies and sadie bahamians Horse hijabs husks jms bans bbs bbs bdb dnc dms msn hdhdhdbhdhdhdhdhdhdhdhdhdhfhdhdhdhdbdbdhdhdbdhdhdhdh
The document discusses harmonic motion and traveling waves. It defines periodic and harmonic motion, and notes that harmonic motion can be described by a sinusoidal function. Hooke's law relating force and displacement in springs is introduced. Equations of motion for simple harmonic oscillators like masses on springs and pendulums are derived. The relationship between wavelength, frequency and propagation velocity is defined for traveling waves. Solutions to the wave equation for strings and their properties are also summarized.
This document discusses simple harmonic motion (SHM). SHM occurs when an object experiences a restoring force proportional to its displacement from equilibrium. This results in sinusoidal oscillations described by x(t) = Acos(ωt + φ), where A is amplitude, ω is angular frequency, and φ is the phase. SHM includes examples like a mass on a spring and a simple pendulum. The relationships between displacement, velocity, acceleration, period, frequency, and energy in SHM systems are explored.
The document discusses simple harmonic motion (SHM), where a particle moves back and forth such that its acceleration is directly proportional to its distance from a fixed point. SHM has the properties that the particle's velocity is zero at the amplitude of its oscillation, and it travels between the points of -a and +a on its axis. Examples are given of particles moving according to SHM equations, and exercises are provided to practice determining SHM, periods of motion, and maximum values.
Application of laplace wave equation in musicLuckshay Batra
This document discusses the application of the Laplace wave equation to music. The Laplace equation is a partial differential equation that can describe wave propagation phenomena. The document presents a problem involving the transverse vibrations of an elastic string that is stretched and fixed at both ends. The solution to this problem is the one-dimensional wave equation. The wave equation and its variants are important for understanding sound wave production and propagation in musical instruments, concert halls, and other spaces.
This document discusses the simple harmonic oscillator. It defines a simple harmonic oscillator as an oscillator that is neither driven nor damped, with motion that is periodic and sinusoidal with constant amplitude. The acceleration of a body in simple harmonic motion is directly proportional to and directed towards the displacement from the equilibrium position. General equations for displacement, velocity, and acceleration as a function of time and other variables are provided. Quantum mechanical treatment of the simple harmonic oscillator is also summarized. Examples of simple harmonic oscillators include a mass on a spring and a simple pendulum in small angle approximation.
The document discusses oscillations and simple harmonic motion. It defines periodic motion, oscillatory motion, and harmonic motion. Harmonic motion can be described using sine and cosine functions. Examples of oscillations include a swinging pendulum and vibrating springs. The period and frequency of oscillations are defined. For simple harmonic motion, the displacement is directly proportional to the displacement from equilibrium and opposite in sign. The velocity and acceleration functions for SHM are derived. For a mass-spring system, the restoring force is proportional to the displacement. The total mechanical energy of a simple harmonic oscillator remains constant over time as the kinetic and potential energy alternately increase and decrease during oscillation.
This document discusses oscillations and wave motion. It begins by introducing mechanical vibrations and simple harmonic motion. It then covers damped and driven oscillations, as well as different oscillating systems like springs, pendulums, and driven oscillations. The document goes on to discuss traveling waves, the wave equation, periodic waves on strings and in electromagnetic fields. It also covers waves in three dimensions, reflection, refraction, diffraction, and interference of waves. Key concepts covered include amplitude, frequency, period, angular frequency, energy of oscillating systems, and resonance.
1. This document contains solutions to problems from Chapter 1 of the textbook "The Physics of Vibrations and Waves".
2. It provides detailed calculations and explanations for problems related to simple harmonic motion, including determining restoring forces, stiffness, frequencies, and solving differential equations of motion.
3. Examples include a simple pendulum, a mass on a spring, and vibrations of strings, membranes, and gas columns.
The document discusses the wave equation and its application to modeling vibrating strings and wind instruments. It describes how the wave equation can be separated into independent equations for time and position using the assumption that displacement is the product of separate time and position functions. This separation leads to trigonometric solutions that satisfy the boundary conditions of strings fixed at both ends. The solutions represent standing waves with discrete frequencies determined by the length, tension, and density of the string. Similar methods apply to wind instruments with different boundary conditions.
This document discusses simple harmonic motion (SHM) and related concepts like angular velocity, restoring forces, displacement, velocity, acceleration, energy, resonance, and damping. It provides equations for angular velocity, SHM acceleration, displacement, velocity, energy, and the simple pendulum. Examples are given and questions provided for practice calculations involving these equations and concepts.
The document discusses key concepts from Einstein's special theory of relativity, including:
1) Frames of reference and the distinction between inertial and non-inertial frames. The laws of motion only hold in inertial frames.
2) The postulates of special relativity - that the laws of physics are the same in all inertial frames, and that the speed of light is constant.
3) Consequences of these postulates, including Lorentz transformations, length contraction, time dilation, and the relativity of simultaneity.
4) Experiments that motivated relativity, like the Michelson-Morley experiment, and equations like Lorentz transformations that were developed to be consistent with the postulates
This document discusses simple harmonic motion and elasticity. It begins by defining simple harmonic motion as back-and-forth motion caused by a restoring force proportional to displacement, with displacement centered around an equilibrium position. It then discusses Hooke's law, where the restoring force of an ideal spring is directly proportional to displacement. Several equations for simple harmonic motion are presented, including those relating displacement, velocity, acceleration, period, frequency, and amplitude. Examples are provided to illustrate these concepts for springs and pendulums undergoing simple harmonic motion.
(1) The document describes a theoretical physics problem involving a pendulum bob suspended from a rigid cylindrical rod. (2) It asks a series of questions about the motion of the pendulum bob and its velocity and acceleration at different points in its swing. (3) It also considers a variation where a heavier weight is attached below the pendulum, causing it to fall as the pendulum swings, and asks for the critical ratio of the weight's fall distance to the total string length needed for the pendulum to swing all the way around the rod.
The slides are designed for my guided study in MSc CUHK.
It is about the brief description on classical mechanics and quantum mechanics .
Some Slides I got from the slideshare clipboards for better illustration of the ideas in Physics. Thanks to slideshare, I make a milestone on presenting one of the prominent fields in modern physics.
The two waves would pass through each other and continue traveling in their original directions. At the point where they meet, both waves would be visible as their displacements add together through superposition. If a crest met a trough, they would undergo destructive interference and cancel each other out at the point where they meet.
This document defines key terms and equations related to simple harmonic motion (SHM). It discusses oscillating systems that vibrate back and forth around an equilibrium point, like a mass on a spring or pendulum. The key parameters of SHM systems are defined, including amplitude, wavelength, period, frequency, displacement, velocity, acceleration. Equations are presented that relate the displacement, velocity, acceleration as sinusoidal functions of time. The concepts of kinetic, potential and total energy are also explained for oscillating systems undergoing SHM.
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
CLASS XII - CHAPTER 5: OSCILLATION (PHYSICS - MAHARASHTRA STATE BOARD)Pooja M
This document provides information about oscillations and simple harmonic motion (SHM). It defines oscillation as periodic motion that repeats after a definite time interval. SHM is described as oscillatory motion where the restoring force is directly proportional to displacement from the equilibrium position. The key characteristics of SHM include:
- The differential equation relating displacement, velocity, and acceleration.
- Expressions for displacement, velocity, and acceleration as functions of time and constants.
- Definitions and calculations of important terms like amplitude, period, frequency, phase.
- Conditions required for motion to be considered SHM.
- Examples of SHM and calculations related to restoring force and period.
Text Book: An Introduction to Mechanics by Kleppner and Kolenkow
Chapter 1: Vectors and Kinematics
-Explain the concept of vectors.
-Explain the concepts of position, velocity and acceleration for different kinds of motion.
References:
Halliday, Resnick and Walker
Berkley Physics Volume-1
Physical Society the sentence but short speech on challenges of educational system in Bangladesh studies and sadie bahamians Horse hijabs husks jms bans bbs bbs bdb dnc dms msn hdhdhdbhdhdhdhdhdhdhdhdhdhfhdhdhdhdbdbdhdhdbdhdhdhdh
This problem involves analyzing the motion of a ball thrown vertically upwards in an elevator shaft, and an open-platform elevator moving upwards at a constant velocity.
The key steps are:
1) Use kinematic equations to find the velocity and position of the ball as a function of time, assuming constant downward acceleration due to gravity.
2) Determine the velocity and position of the elevator as a constant upward velocity.
3) Express the relative motion of the ball with respect to the elevator to determine when they meet.
By setting the position of the ball equal to the position of the elevator and solving for time, we can determine when the ball and elevator meet at 26.4 seconds after the ball is thrown
Classical mechanics failed to explain certain phenomena observed at the microscopic level like black body radiation and the photoelectric effect. This led to the development of quantum mechanics, with key aspects being the wave function Ψ, Schrodinger's time-independent and time-dependent wave equations, and operators like differentiation that act on wave functions to produce other wave functions. The wave function Ψ relates to the probability of finding a particle, with |Ψ|2 representing the probability.
This document discusses the reflection and transmission of waves at the junction of two strings with different linear densities. It provides equations relating the amplitudes of the incident, reflected, and transmitted waves based on the continuity of displacement and slope at the junction. It also discusses sound as a pressure wave and derives an expression for the speed of sound in a fluid from the definition of pressure as a cosine wave. Finally, it defines the loudness of sound in decibels and calculates differences in loudness for different sound intensities.
1. The lecture goals were to describe oscillations and simple harmonic motion, analyze them using energy concepts, and apply SHM to different physical situations like pendulums and driving forces.
2. The document then covered topics like equilibrium, restoring forces, characteristics of periodic motion, and the mathematics of simple harmonic oscillators.
3. It concluded by discussing mechanical waves, including transverse and longitudinal waves, wave speed, interference, and standing waves on a string.
CBSE Physics/ Lakshmikanta Satapathy/ Wave theory/ path difference and Phase difference/ Speed of sound in a gas/ Intensity of wave/ Superposition of waves/ Interference of waves
Motion in a Straight Line Class 11 Physics
As students embark on the journey into the fascinating realm of physics in Class 11, one of the fundamental topics that captivates their attention is "Motion in a Straight Line." This foundational concept forms the bedrock of kinematics, the branch of physics concerned with the description of motion. In this chapter, students explore the dynamics of objects moving along a linear path, unraveling the principles that govern their displacement, velocity, and acceleration. From understanding the basic distinctions between scalar and vector quantities to delving into the equations that quantify motion, Class 11 students embark on a captivating exploration of the fundamental laws that underpin the linear journey of objects in motion. Motion in a straight line not only serves as a gateway to more intricate concepts in physics but also provides a lens through which students perceive and analyze the dynamics of the world around them.
For more information, visit. www.vavaclasses.com
1) The document presents three theoretical physics problems involving spinning balls, charged particles in loops, and laser cooling of atoms.
2) Problem 1 considers a spinning ball falling and rebounding, calculating the rebound angle, horizontal distance traveled, and minimum spin rate. Problem 2 analyzes relativistic effects on charged particles in a moving loop in an electric field.
3) Problem 3 describes using lasers to cool atoms by resonant absorption. It calculates the laser frequency needed, velocity range absorbed, direction change upon emission, maximum velocity decrease, number of absorption events to slow to zero velocity, and distance traveled during cooling.
The document discusses wave energy and interference. It defines standing waves as occurring when a traveling wave is reflected by a fixed boundary, resulting in the superposition of the original wave and reflected wave. Standing waves have nodes where the displacement is always zero, and antinodes where the displacement is at a maximum. The normal modes of a system are its allowed standing wave patterns, which are determined by the boundary conditions. For a string fixed at both ends, the normal modes are half-wavelengths that are integer multiples of the string length.
The speed of transverse waves on a string depends only on the ratio of tension to linear mass density. Doubling the tension and halving the linear mass density results in the same ratio, so the wave speed is unchanged. The speed in the second string is 2v.
1. This document discusses key concepts related to oscillations and waves including: simple harmonic motion (SHM), parameters that describe SHM like amplitude, period, frequency, phase, and the relationships between displacement, velocity, and acceleration in SHM.
2. Examples of SHM include a mass on a spring and a simple pendulum. The frequency and period of oscillations can be determined from the properties of the object and spring/pendulum.
3. Forced oscillations and resonance are explored where a driving force can excite the natural frequency of an object, causing large oscillations. This can be useful or destructive depending on the situation.
Introduction to oscillations and simple harmonic motionMichael Marty
Physics presentation about Simple Harmonic Motion of Hooke's Law springs and pendulums with derivation of formulas and connections to Uniform Circular Motion.
References include links to illustrative youtube clips and other powerpoints that contributed to this peresentation.
1) The document discusses transmission lines and their characteristics. It describes different types of transmission lines including coaxial lines, two-wire lines, and microstrip lines.
2) It presents the telegrapher's equations which model voltage and current on a transmission line as a function of position and time. These equations include parameters like inductance and capacitance per unit length.
3) Waves can propagate down transmission lines, maintaining their shape as they travel at a characteristic velocity. The wavelength depends on the wave velocity and frequency. Phasors are used to represent sinusoidal waves independent of time.
The document discusses simple harmonic motion (SHM). SHM describes the motion of an object undergoing periodic motion where the restoring force is directly proportional to the displacement from equilibrium. Examples of SHM include a block attached to a spring and vibrating musical strings. The motion can be modeled mathematically using Hooke's law and expressed as a sinusoidal function of time. Key characteristics of SHM include the period, frequency, amplitude, and phase of the oscillations. Graphs of position, velocity, and acceleration versus time for an object in SHM are also sinusoidal.
1. The document discusses motion in a straight line, including key concepts like displacement, average and instantaneous velocity, acceleration, position-time and velocity-time graphs.
2. It provides equations for uniformly accelerated motion relating position, velocity, time, and acceleration.
3. Examples of relative motion and relative velocity between two objects moving with different average velocities along the same axis are given.
This document discusses different types of mechanical waves and their properties. It defines mechanical waves as oscillations that transfer energy through a medium. Key points include:
- Mechanical waves can be transverse (perpendicular to direction of travel) or longitudinal (parallel to direction of travel).
- They transport energy through the medium and require a medium, like air or water, to propagate.
- Examples of mechanical waves include water waves, sound waves, and waves on a string or rope.
- Harmonic waves have a sinusoidal shape described by a mathematical function involving amplitude, wavelength, frequency, and phase.
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
1) The document defines harmonic waves as waves that travel in simple harmonic motion. It describes properties such as amplitude, wavelength, frequency, period, and wave speed.
2) Equations are provided that describe the displacement of a medium over time for waves traveling in increasing or decreasing x directions.
3) The velocity and acceleration of segments of a medium are defined in terms of the displacement equation and its derivatives.
JEE Physics/ Lakshmikanta Satapathy/ Work Energy and Power/ Force and Potential energy/ Angular momentum and Speed of Particle/ MCQ one or more correct
JEE Physics/ Lakshmikanta Satapathy/ MCQ On Work Energy Power/ Work-Energy theorem/ Work done by Gravity/ Work done by Air resistance/ Change in Kinetic Energy of body
CBSE Physics/ Lakshmikanta Satapathy/ Electromagnetism QA/ Magnetic field due to circular coil at center & on the axis/ Magnetic field due to Straight conductor/ Magnetic Lorentz force
1) Four point charges placed at the corners of a square were given. The total electric potential at the center of the square was calculated to be 4.5 x 10^4 V.
2) The electric field and potential due to a point charge were given. Using these, the distance of the point from the charge and the magnitude of the charge were calculated.
3) An oil drop carrying a charge between the plates of a capacitor was given. The voltage required to balance the drop, given the mass and distance between plates, was calculated to be 9.19 V.
1) Vibrations in air columns inside closed and open pipes produce standing waves with characteristic frequencies called harmonics or overtones.
2) In closed pipes, only odd harmonics like the fundamental, 1st overtone (3rd harmonic) and 2nd overtone (5th harmonic) are possible. In open pipes, all harmonics including the fundamental, 1st overtone (2nd harmonic) and 2nd overtone (3rd harmonic) are observed.
3) There is an end correction of about 0.3 times the pipe diameter that must be added to the effective pipe length to account for vibrations outside the physical opening.
4) The speed of sound in air can be measured
CBSE Physics/ Lakshmikanta Satapathy/ Wave Motion Theory/ Reflection of waves/ Traveling and stationary waves/ Nodes and anti-nodes/ Stationary waves in strings/ Laws of transverse vibration of stretched strings
JEE Mathematics/ Lakshmikanta Satapathy/ Definite integrals part 8/ JEE question on definite integral involving integration by parts solved with complete explanation
JEE Physics/ Lakshmikanta Satapathy/ Question on the magnitude and direction of the resultant of two displacement vectors asked by a student solved in the slides
JEE Mathematics/ Lakshmikanta Satapathy/ Quadratic Equation part 2/ Question on properties of the roots of a quadratic equation solved with the related concepts
JEE Mathematics/ Lakshmikanta Satapathy/ Probability QA part 12/ JEE Question on Probability involving the complex cube roots of unity is solved with the related concepts
JEE Mathematics/ Lakshmikanta Satapathy/ Inverse trigonometry QA part 6/ Questions on Inverse trigonometric functions involving tan inverse function solved with the related concepts
This document contains two problems from inverse trigonometry. The first problem involves finding the values of x and y given trigonometric expressions involving tan(x) and tan(y). The second problem proves the identity x = -x + pi for x in the range (-pi, pi). Both problems are solved step-by-step using trigonometric identities and properties. The document also provides contact information for the physics help website.
This document discusses the transient current in an LR circuit with two inductors (L1 and L2) and a resistor connected to a 5V battery. It provides the equations for calculating the transient current in an LR circuit. It then calculates that for L1, the ratio of maximum to minimum current (Imax/Imin) is 8. Similarly, for L2 the ratio is 5. The total maximum current drawn from the battery is 40A and the minimum is 5A, giving a ratio of 8.
JEE Physics/ Lakshmikanta Satapathy/ Electromagnetism QA part 7/ Question on doubling the range of an ammeter by shunting solved with the related concepts
JEE Mathematics/ Lakshmikanta Satapathy/ Binomial theorem part 6/ JEE Question on the coefficient of a given power of x in the expansion of 100 factors
JEE Physics/ Lakshmikanta Satapathy/ Laws of Motion QA part 7/ Question on Breaking stress of wire connected in a pulley block system solved with the related concepts
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
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Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
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Wave Motion Theory Part1
1. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Wave function
Formation of Waves in a string
Sinusoidal Wave Functions
Condition for Wave Function
Particle velocity and slope
2. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Wave Motion :
It is a kind of disturbance which travels through a material medium due to
repeated periodic vibration of the particles of the medium about their mean
positions, the disturbance being handed over from one particle to the next without
any net transport of the medium.
Transverse Waves :
Particles of the medium execute SHM about their mean position
in a direction perpendicular to the direction of propagation of the
wave. It travels through a medium in the form of crests and
troughs.
Longitudinal Waves :
Particles of the medium execute SHM about their mean position
in the direction of propagation of the wave. It travels through a
medium in the form of compressions and rarefactions.
3. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Formation of a Wave in a stretched string :
String fixed at P and held by
hand at O. Set into periodic
motion with time period T.
(i) After ¼ time period
(ii) After ½ time period
(iii) After ¾ time period
(iv) After one time period
(O moved up and disturbance reached A)
(O moved down to mean position, A moved up and
disturbance reached B)
(O moved down, A moved down, B moved up and
disturbance reached C)
(O moved up, A moved down, B moved down, C
moved up and disturbance reached D)
O P
O P
O P
O P
O PT
4T
2T
3 4T
0t
x 0 /4 /2 3/4
O A B C D
4OA AB BC CD
OD
4. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Wave Function : A wave pulse is moving along +ve x-direction with speed (v) as
shown in figure. Particles of the medium oscillate in SHM along y–direction
O Px
Displacement of particle at position x and time t = y(x ,t)
It is a function of both x and t . We need to define this function.
At O , displacement = y(0,t) (depends on t only)
(0, ) ( ) ... (1)y t f t We write
The same displacement occurs at P at time (t + x/v)
[ When position increases by x , time increases by x/v ]
( , ) (0, )y x t x v y t
5. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Eqn. of a wave propagating in the +ve x–direction is given by
( , ) ( ) ... (3)y x t f vt x
Eqn. of a wave propagating in the – ve x-direction is given by
( , ) ( ) ... (4)y x t f vt x
In general , we write ( , ) ( ) ... (5)y x t f vt x
Using eqn.(1) we get ( , ) ( ) . . . (2)y x t f t x v
Since v is const. we can write ( , ) ( )y x t f vt x
Similarly , displacement y(x .t) at P was at O at time (t – x/v)
[ When position decreases by x , time decreases by x/v ]
( , ) (0, )y x t y t x v
6. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Condition for Wave Function :
(2) ( , ) ( )y x t f t x v
Partially differentiating w.r.to t
( ).(1) ( ) . . . (6)
y
f t x v f t x v
t
Again partially differentiating w.r.to t
2
2
( ).(1) ( ) . . . (7)
y
f t x v f t x v
t
Partially differentiating w.r.to x
1 1
( ).( ) ( ) . . . (8)
y
f t x v f t x v
x v v
Again partially differentiating w.r.to x
2
2 2
1 1 1
( ).( ) ( ) . . . (9)
y
f t x v f t x v
x v v v
7. Physics Helpline
L K Satapathy
Wave Motion Theory 1
2
2
(7) ( )
y
f t x v
t
2
2 2
1
(9) ( )
y
f t x v
x v
2 2
2 2 2
1
. . . (10)
y y
x v t
[particle velocity]
. . . (11)
y y
v
t x
Also [slope]
Relation between particle velocity and slope
(6) ( )
y
f t x v
t
1
(8) ( )
y
f t x v
x v
Necessary condition for a
function to represent a wave
Particle velocity = – (Wave velocity)(Slope)
8. Physics Helpline
L K Satapathy
Wave Motion Theory 1
O
v
Consider a wave propagating along +ve x-direction
Also from the figure it can be seen that slope at O is +ve
A crest has passed point O.
Particle velocity = – (+ve)(+ve) = – ve
It has to be followed by a trough
Understanding from graph
Wave velocity (v) is +ve
(11)
y y
v
t x
Alternate method :
Particle at O will move downward
Particle velocity at O is – ve
9. Physics Helpline
L K Satapathy
Wave Motion Theory 1
Sinusoidal Wave Functions :
(2) ( , ) ( )y x t f t x v
We write sin ( ) . . . (12)y A t x v
Relations to be used :
2 2
, 2K T K v
T T K
(12) sin sin( ) . . . (13)y A t x y A t Kx
v
2 2
(13) sin sin2 . . . (14)
t x
y A t x y A
T T
2 2
(14) sin sin . . . (15)y A t x y A vt x
T
[ /v = K]
10. Physics Helpline
L K Satapathy
Wave Motion Theory 1
O x
Illustration :
The figure shows a sinusoidal wave , propagating in
the positive x-direction in a string at t = 0. Then
which of the following equations represents the wave.
( ) sin( ) ( ) sin( )a y A t kx b y A kx t
( ) cos( ) ( ) cos( )c y A t kx d y A kx t
Soln. : For the wave in the fig. y = 0 at x = 0 and t = 0
Again , (11) particle velocity = – (wave velocity)(slope)
Both wave velocity and slope are +ve at x = 0 particle velocity is – ve
( ) cos( ) cos( ) ( 0)
y
a A t kx A t ve at x
t
[ (a) is incorrect]
( ) cos( ) cos( ) ( 0)
y
b A kx t A t ve at x
t
[ (b) is correct]
[ (c) & (d) are incorrect]For both (c) & (d) , y = A cos (0) = A [at x = 0 & t = 0]
11. Physics Helpline
L K Satapathy
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