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Waves carry energy through a medium without transporting the medium itself. This motion of energy is called a wave. A pulse is a short-duration disturbance from equilibrium that can move as a wave through a medium. The displacement of a pulse from equilibrium over time and position can be described mathematically. The equation D(x,t) defines the displacement D of a pulse at position x and time t. This allows calculating the displacement over time as a pulse moves through a medium at a given velocity.
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This document defines and explains standing waves. A standing wave results from two identical waves traveling in opposite directions with the same frequency. When the frequency is resonant, the waves will superimpose to form a stationary pattern with antinodes of maximum displacement and nodes of zero displacement. The position of nodes and antinodes can be determined using the standing wave equation. For a guitar string example, the document calculates the amplitude and wavelength of the traveling wave, finds the positions of the first two nodes, and determines the first harmonic frequency.
Standing waves
Here are the answers to the lab preparation problems:
1. A wave on the water surface is a transverse wave. The oscillation of the water surface is perpendicular to the direction of wave propagation.
2. The wavelength of visible light ranges from 400-800nm. Using the formula c=fλ, where c is the speed of light (3x108 m/s), we can calculate:
f = c/λ
f = (3x108 m/s) / (400x10-9 - 800x10-9) m
f = 7.5x1014 - 3.75x1014 Hz
3. A standing wave is produced with a frequency of 60 Hz. The
Free vibrations
This document provides an overview of natural vibrations with one degree of freedom. It defines key terms like degrees of freedom, simple harmonic motion, angular frequency, and periodic time. Examples of natural vibrations covered include a simple pendulum, a mass on a spring, and beams experiencing transverse vibrations. Methods for analyzing natural vibrations include Rayleigh's energy method and Dunkerley's method for combining frequencies from distributed and point loads. Worked examples are provided to illustrate calculating displacement, velocity, and acceleration of bodies in simple harmonic motion.
Wk 1 p7 wk 3-p8_13.1-13.3 & 14.6_oscillations & ultrasound
This document discusses oscillations and simple harmonic motion. It begins by listing learning outcomes related to oscillations, including describing examples of free and forced oscillations. It then provides definitions and equations related to simple harmonic motion, such as the defining equation a=-ω2x. Graphs of displacement, velocity, and acceleration over time for simple harmonic motion are shown. Examples of the simple pendulum and a mass on a spring are provided to illustrate simple harmonic motion. The document also discusses the kinetic and potential energy changes that occur during simple harmonic motion.
Harmonic Waves
A harmonic wave is a wave that undergoes simple harmonic motion as it travels. It can be described by the equation D(x,t)=Asin(kx-wt+φ), where D is displacement, A is amplitude, k is wave number, w is angular frequency, x is position, t is time, and φ is phase. The document provides examples of how to use this equation to calculate properties like wavelength, frequency, and acceleration of a harmonic wave traveling through different media. It also includes sample problems solving for these wave properties given values for variables like velocity, frequency, amplitude, and position over time.
Learning object 1 travelling waves
The document describes the movement of travelling waves through a medium. It defines key concepts such as pulses, displacement, and speed. It provides an analogy of a wave moving through a crowd at a sports game. The key equation given relates the displacement of a point on the medium to the distance and time: D(x,t) = D(x-vt). It then works through an example problem applying this equation to find the displacement of a marked point on a rope at a given time, as well as determining when the maximum displacement occurs for a different point. Finally, it discusses how the speed of a wave depends on the tension and linear mass density of the medium.
Basics in Seismology
This document discusses the basic principles of seismic waves. It introduces longitudinal (P) waves and shear (S) waves, and derives the one-dimensional wave equation. It discusses wave phenomena like reflection, transmission, and refraction based on Snell's law at boundaries between layers. It also discusses the different arrivals of direct, reflected, and refracted/head waves that can be measured at the surface for seismic exploration purposes.
Position and time plots learning objective
This learning object aims to explore the relationship between position plots and time plots. I initially struggled to comprehend the distinction between the two plots. However, I was able to reach an understanding after some research and practice. Hopefully my learning objective can help other students gain a better understanding of this topic as well!
Fourier series pgbi
Fourier series are used to represent periodic functions as the sum of simple oscillating functions like sines and cosines. This allows periodic functions, including discontinuous ones, to be broken down into their constituent frequencies or harmonics. Applications include representing sound waves, light waves, radio signals, and other physical phenomena involving wave motion or vibration. The Fourier coefficients determine the relative importance of each harmonic in the overall signal.
Standing waves
1. A standing wave is formed by two waves of equal amplitude, wavelength, and frequency travelling in opposite directions in the same medium.
2. Nodes occur at positions where the amplitude is zero, while antinodes occur at positions of maximum amplitude. The distance between nodes is half the wavelength, and between a node and adjacent antinode is a quarter wavelength.
3. For a string fixed at both ends, standing waves can form with wavelengths of 2L/m, where L is the string length and m is a positive integer. The lowest frequency is called the fundamental frequency. Higher integer multiples of this frequency are the harmonics.
Vibration and WavesT = 2pisqrt(mk)v = lambdafp = A sin(kx.pdf
Vibration and Waves
T = 2pi*sqrt(m/k)
v = lambda*f
p = A sin(kx-wt) w=2*pi*f (pressure in travelling sound wave), k = 2pi/lambda, A = amplitude,
x = displacement.
1. Periodic motion: used to describe a vibration or an oscillation that repeats itself over the same
path.. Displacement: The position of an object. Amplitude: The maximum displacement. Period:
The time in seconds required for one complete cycle. Frequency: The number of cycles, per
second. Simple Harmonic Motion: Sinusoidal motion of a single frequency.
2. Total E = 1/2kA^2. = 1/2kx^2+1/2mv^2. EPE = 1/2kx^2.
3. The equation for the period of a spring is T = 2pi*sqrt(m/k). For example, how long does it
take for a spring with a hanging mass of 5 kg and spring constant 10N/m to exhibit one complete
cycle? T = 2pi*sqrt(5/10). T = 2pi*sqrt(1/2).
4. Since a period is the time it takes for one complete cycle in seconds, frequency is the inverse
of the period. f = 1/T. T = 1/f.
5. For describing the motion generated SHM, you can use x = A sin 2pi*f*t. This is if the motion
starts at equilibrium point. If it starts at the crest/trough of its motion, then use x = A cos 2pi*f*t.
6. For describing the motion generated SHM, you can use x = A sin 2pi*f*t. This is if the motion
starts at equilibrium point. If it starts at the crest/trough of its motion, then use x = A cos 2pi*f*t.
7. The maximum velocity of a particle on SHM can be found by v = 2pi*A*f. Now, for any other
velocity at a point in time, it can be found by v = v0(sqrt(1-x^2/A^2)).
8. The equation for the period of a pendulum is T = 2*pi*sqrt(L/g). L = length of the pendulum.
This only works if its amplitude is small and friction can be ignored.
9. Dampened harmonic motion is the gradual decrease of maximum displacement. This is caused
by the presence of frictional forces. The energy is eventually all transformed to heat.
10. Forced vibration is due to an external source, which applies its own frequency to the spring.
The natural frequency of the spring is actually 1/2pi * sqrt(k/m), which is what it will actually
vibrate at without external force.
11. Amplitude denotes the distance between the equilibrium and the crest or trough of the wave.
Wavelength is the distance from one point of the wave to the corresponding point in the next
cycle. (crest-crest). This can be found be lambda = v/f. Wave velocity is the velocity at which
wave crests move. V = lambda*f. Node is referring to the point of destructive interference.
Antinode is referring to the point of constructive interference.
12. The relationship between velocity, wavelength, and frequency is v = lambda*f, where
lambda is the wavelength and f is the frequency, v is the wave velocity.
13. A transverse wave refers to a wave that causes the particles of the medium it travels in to
move a direction perpendicular to the motion of the wave itself. On the other hand, in a
longitudinal wave, the vibration of the particles of the medium is along the same direction as the
motion of the wa.
9.1 shm
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.
Harmonic waves
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.
Lec1 Ocsillation and Waves
Oscillations are ubiquitous in nature and occur in many systems when disturbed from equilibrium. The document introduces the simple harmonic oscillator (SHO) model to describe small oscillations near equilibrium. A SHO undergoes sinusoidal oscillations with an angular frequency that depends on the spring constant and mass. Complex numbers provide a useful way to represent the amplitude and phase of oscillations. The SHO model applies to many systems locally, as potentials can often be approximated as quadratic near equilibrium points.
waves and wave properties clem_waves_lesson02_presentation.ppt
A presentation on wave and wave properties
waves ppt.ppt
Waves are disturbances that transfer energy through a medium from one point to another without transferring matter. There are two main types of waves: transverse waves, where the medium moves perpendicular to the wave direction, and longitudinal waves, where the medium moves parallel to the wave direction. Key wave properties include wavelength, frequency, amplitude, and speed. The energy of a wave depends on its amplitude, with higher amplitudes corresponding to more energy. Waves can change direction through reflection at surfaces, refraction when entering a new medium, and diffraction bending around obstacles.
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The debris of the ‘last major merger’ is dynamically young
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
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As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
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be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
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Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
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among stars.
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Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
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s
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. The X-ray sources exhibit a highly concentrated spatial distribution,
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Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
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原版制作(carleton毕业证书)卡尔顿大学毕业证硕士文凭原版一模一样
原版纸张【微信：741003700 】【(carleton毕业证书)卡尔顿大学毕业证】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
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1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
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7:个人信誉贷款加10分
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Slides from:
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Track: Artificial Intelligence
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mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
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Learning o 1
- 1. Key Points: *Waves carry energy As a wave travels along a string, air or any medium form, energy is created and travels through the medium. We can consider this as a wave is a motion of energy through a medium *The wave travels through the medium A wave does not carry its medium with it, instead, the medium willmove out of its equilibrium position. For example, during an earthquake, damage to surroundings is caused due to the ground moving out of equilibrium.
- 2. Consider: What is a pulse? A pulse can be defined as an equilibrium disturbance in a wave for a short duration. For example, a single knock on a door creates a sound pulse that lasts a short amount of time. If a string is held under constant tension, we can analyze the motion of the string with respect to a point.
- 3. Calculatingvariables in a Pulse In 1D *The equilibrium of a pulse is denoted by D(x, t) D = displacement from equilibrium (m) x = position (m) t= time (s) *We can use this equation to describe a waveform. At a certaintime during a pulse, different waveforms are present. *Consider the function D(x, t) = 6 𝑥2+4 *If a pulse has a position of x = 2.0m at 0.0s, what is the equation? Answer: x=2.0m, t=0.0s: D(2.0m, 0.0s) = 6 (2.0𝑚)2+4
- 4. DISPLACEMENT FUNCTION *How about at 1.5s if it is moving at 3.0m/s to the left? At any speed, we can substitute x for (x-vt). Why? If at t=0, the wave of a pulse is moving at an increasing x with speed v, then we can make this substitution. This is called the displacement function Answer: D(x, 1.5s) = 6 ( 𝑥−𝑣𝑡)2+4 Plug in t=1.5s and v = -3.0m/s D(x, 1.5s) = 6 ( 𝑥+3.0(1.5))2+4 *Remember, since x-vt represents a positive velocity, x+vt will represent a negative velocity. peak Example of a waveform function when t=1.0s
- 5. Try: A travelling pulse is given by: D(x, t) = 2.0 ( 𝑥−3.0𝑡)4+5.0 a) What is the velocity of the pulse? b) What is the displacement of a point on the medium at x = 1.5m at t=2.0s Answer: a) remember, x-vt velocity = 3.0m/s to the right b)Plug in values: D(1.5, 2.0) = 20.0 (1.5−3.0(2.0))4+5.0 D = 4.8e-2m