Phyisics explaination on simple harmonic motion for first and second year university students , includes practical and theory about waves and some practical applications
Topic of computational methods for mechanical engineering. Information about spring mass system. Mathematical modelling of spring mass system. free mass spring system. Damped vibration. Forced damped system. Free oscillation.
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.
Topic of computational methods for mechanical engineering. Information about spring mass system. Mathematical modelling of spring mass system. free mass spring system. Damped vibration. Forced damped system. Free oscillation.
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.
Fundamentasl of Physics "CENTER OF MASS AND LINEAR MOMENTUM"Muhammad Faizan Musa
9-1 CENTER OF MASS
fter reading this module, you should be able to . . .
9.01 Given the positions of several particles along an axis or
a plane, determine the location of their center of mass.
9.02 Locate the center of mass of an extended, symmetric
object by using the symmetry.
9.03 For a two-dimensional or three-dimensional extended object with a uniform distribution of mass, determine the center
of mass by (a) mentally dividing the object into simple geometric figures, each of which can be replaced by a particle at its
center and (b) finding the center of mass of those particles.
9-2 NEWTON’S SECOND LAW FOR A SYSTEM OF PARTICLES
After reading this module, you should be able to . . .
9.04 Apply Newton’s second law to a system of particles by relating the net force (of the forces acting on the particles) to
the acceleration of the system’s center of mass.
9.05 Apply the constant-acceleration equations to the motion
of the individual particles in a system and to the motion of
the system’s center of mass.
9.06 Given the mass and velocity of the particles in a system,
calculate the velocity of the system’s center of mass.
9.07 Given the mass and acceleration of the particles in a
system, calculate the acceleration of the system’s center
of mass.
9.08 Given the position of a system’s center of mass as a function of time, determine the velocity of the center of mass.
9.09 Given the velocity of a system’s center of mass as a
function of time, determine the acceleration of the center
of mass.
9.10 Calculate the change in the velocity of a com by integrating the com’s acceleration function with respect to time.
9.11 Calculate a com’s displacement by integrating the
com’s velocity function with respect to time.
9.12 When the particles in a two-particle system move without the system’s commoving, relate the displacements of
the particles and the velocities of the particles,
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
7-1 KINETIC ENERGY
After reading this module, you should be able to . . .
7.01 Apply the relationship between a particle’s kinetic
energy, mass, and speed.
7.02 Identify that kinetic energy is a scalar quantity.
7-2 WORK AND KINETIC ENERGY
After reading this module, you should be able to . . .
7.03 Apply the relationship between a force (magnitude and
direction) and the work done on a particle by the force
when the particle undergoes a displacement.
7.04 Calculate work by taking a dot product of the force vector and the displacement vector, in either magnitude-angle
or unit-vector notation.
7.05 If multiple forces act on a particle, calculate the net work
done by them.
7.06 Apply the work–kinetic energy theorem to relate the
work done by a force (or the net work done by multiple
forces) and the resulting change in kinetic energy. etc...
Fundamentasl of Physics "CENTER OF MASS AND LINEAR MOMENTUM"Muhammad Faizan Musa
9-1 CENTER OF MASS
fter reading this module, you should be able to . . .
9.01 Given the positions of several particles along an axis or
a plane, determine the location of their center of mass.
9.02 Locate the center of mass of an extended, symmetric
object by using the symmetry.
9.03 For a two-dimensional or three-dimensional extended object with a uniform distribution of mass, determine the center
of mass by (a) mentally dividing the object into simple geometric figures, each of which can be replaced by a particle at its
center and (b) finding the center of mass of those particles.
9-2 NEWTON’S SECOND LAW FOR A SYSTEM OF PARTICLES
After reading this module, you should be able to . . .
9.04 Apply Newton’s second law to a system of particles by relating the net force (of the forces acting on the particles) to
the acceleration of the system’s center of mass.
9.05 Apply the constant-acceleration equations to the motion
of the individual particles in a system and to the motion of
the system’s center of mass.
9.06 Given the mass and velocity of the particles in a system,
calculate the velocity of the system’s center of mass.
9.07 Given the mass and acceleration of the particles in a
system, calculate the acceleration of the system’s center
of mass.
9.08 Given the position of a system’s center of mass as a function of time, determine the velocity of the center of mass.
9.09 Given the velocity of a system’s center of mass as a
function of time, determine the acceleration of the center
of mass.
9.10 Calculate the change in the velocity of a com by integrating the com’s acceleration function with respect to time.
9.11 Calculate a com’s displacement by integrating the
com’s velocity function with respect to time.
9.12 When the particles in a two-particle system move without the system’s commoving, relate the displacements of
the particles and the velocities of the particles,
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
7-1 KINETIC ENERGY
After reading this module, you should be able to . . .
7.01 Apply the relationship between a particle’s kinetic
energy, mass, and speed.
7.02 Identify that kinetic energy is a scalar quantity.
7-2 WORK AND KINETIC ENERGY
After reading this module, you should be able to . . .
7.03 Apply the relationship between a force (magnitude and
direction) and the work done on a particle by the force
when the particle undergoes a displacement.
7.04 Calculate work by taking a dot product of the force vector and the displacement vector, in either magnitude-angle
or unit-vector notation.
7.05 If multiple forces act on a particle, calculate the net work
done by them.
7.06 Apply the work–kinetic energy theorem to relate the
work done by a force (or the net work done by multiple
forces) and the resulting change in kinetic energy. etc...
Prudent® Citrus chelated micronutrients solution is formulated with Krystal Klear®
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Ирина Мирошник | Роль упаковки в сохранении продуктов питанияUkrplastic
Выступление Ирины Мирошник на конференции "Упаковка Украины и инициатива Save Food", проведенной в рамках выставки ПАК ЭКСПО 2016 (Киев), 12-14 апреля 2016 года.
El Mundo - Seducidos por campus extranjerosJack Nicholls
Cada vez son más los alumnos que apuestan por realizar sus estudios superiores en el extranjero debido a las expectativas laborales del mercado global…
ASSA ABLOY customer cases 2013 corporate presentation part 3ASSA ABLOY
Through a few real examples, we hope to show you the width of customers who choose ASSA ABLOY to help them with their security solutions.and locking needs. This is the third part of the 2013 Corporate Presentation. The other parts are Facts and Figures and Sustainability.
ASSA ABLOY's facts and figures 2013 Corporate Presentation part 1ASSA ABLOY
ASSA ABLOY's Corporate Presentation is designed to give an overview of the Group's business. This part presents Facts and Figures. The complete presentation comprises two more parts: Customer Cases and Sustainability, also available here on SlideShare.
This paper presents the Physics Rotational Method of the simple gravity pendulum, and it also applies Physics Direct Method to represent these equations, in addition to the numerical solutions discusses. This research investigates the relationship between angular acceleration and angle to find out different numerical solution by using simulation to see their behavior which shows in last part of this article.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
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1. Experiment 11: Simple Harmonic Motion
Figure 11.1
EQUIPMENT
Spring
Metal Ball
Wood Ball
(Note: sharp hooks)
Meter Stick
Digital Balance
Stopwatch
Pendulum Clamp and Rod
String
Masses: (2) 100g, (1) 50g
Mass Hanger
Table Clamp
Protractor
57
2. 58 Experiment 11: Simple Harmonic Motion
Advance Reading
Text: Simple harmonic motion, oscillations, wave-
length, frequency, period, Hooke’s Law.
Lab Manual: Appendix B
Objective
To investigate simple harmonic motion using a simple
pendulum and an oscillating spring; to determine the
spring constant of a spring.
Theory
Periodic motion is “motion of an object that regularly
returns to a given position after a fixed time inter-
val.” Simple harmonic motion is a special kind of peri-
odic motion in which the object oscillates sinusoidally,
smoothly. Simple harmonic motion arises whenever
an object is returned to the equilibrium position by a
restorative force proportional to the object’s displace-
ment.
F = kx (11.1)
The illustrative example above is Hooke’s Law, which
describes the restorative force of an oscillating spring
of sti↵ness k (spring constant).
For an ideal, massless spring that obeys Hooke’s
Law, the time required to complete an oscillation (pe-
riod, T, seconds) depends on the spring constant and
the mass, m, of an object suspended at one end:
T = 2⇡
r
m
k
(11.2)
The inverse of period is the frequency of oscillation.
Recall that frequency, f, is the number of oscillations
completed by a system every second. The standard
unit for frequency is hertz, Hz (inverse second, s-1
).
The period of oscillation of an ideal, simple pendulum
depends on the length, L, of the pendulum and the
acceleration due to gravity, g:
T = 2⇡
s
L
g
(11.3)
When setting the pendulum in motion, small displace-
ments are required to ensure simple harmonic motion.
Large displacements exhibit more complex, sometimes
chaotic, motion. Simple harmonic motion governs
where the small angle approximation is valid:
Figure 11.2: Small Angle Approximation
The arc length, s, of a circle of radius r is:
s = r (11.4)
When is small, the arc length is approximately equal
to a straight line segment that joins the two points.
Therefore, the following approximations are valid:
⇡ sin ⇡ tan (11.5)
3. Prelab 11: Simple Harmonic Motion 59
Name:
1. Define simple harmonic motion. What conditions must be met? (20 pts)
2. What physical phenomenon does the relationship T = 2⇡
pm
k describe? (20 pts)
3. What physical phenomenon does the relationship T = 2⇡
q
L
g describe? (20 pts)
4. The following data were collected for Part 1 of the lab procedure. Complete the table. The force is due to the
gravitational force. All distances are measured from the bottom of the hanger to the top of the stool. You should
ignore the initial weight of the hanger. Note that x is the change from initial position, xf x0, not the change
from the previous position, x2 x1. (40 pts)
Mass (g) Height (cm) x (m) Force (N)
0 57.5 0 0
100 46.5
200 36.5
300 25.5
400 15.5
500 4.5
4. 60 Experiment 11: Simple Harmonic Motion
PROCEDURE
PART 1: Spring Constant - Hooke’s Law
1. Hang the spring from the pendulum clamp and hang
the mass hanger from the spring. Place a stool un-
der the hanger and measure the initial height x0
above the stool.
2. Add 50 g to the mass hanger and determine the
change in position caused by this added weight.
3. Add 50 g masses incrementally until 250 g has been
added to the mass hanger. Determine the total dis-
placement and the total added weight with each ad-
dition.
4. Generate a graph of F vs. x using Graphical Anal-
ysis. Analyze the graph with a linear fit; print a
copy for each partner.
PART 2: Spring Constant - Oscillation
5. Measure the mass of the spring, mass hanger, and
100 g mass.
Note: The spring used for this experiment is not ideal;
its mass a↵ects the period of oscillation. Account for
this by adding 1/3 the mass of the spring to the value
of suspended mass, m, in your calculations.
6. Hang the spring from the pendulum clamp. Hang
the mass hanger + 100 g from the spring (refer to
Fig. 11.1).
7. Pull the mass hanger down slightly and release it
to create small oscillations. Measure the time re-
quired for 20 oscillations. (This is like measuring
one period twenty times over.)
8. Calculate the period for the oscillating spring.
9. Calculate the spring constant of the spring using
your knowledge of the object’s mass and period of
oscillation.
PART 3: Simple Pendulum
10. Measure the mass of the metal ball.
11. Construct a simple pendulum 100.0 cm in length us-
ing the metal ball and some string. (L is measured
from the center of mass of the ball.)
12. Move the pendulum from equilibrium (about 10 -
20 ) and release it. Measure the time required for
20 oscillations.
13. Determine the period. Record it in the table pro-
vided.
T =
time required
20 cycles
(11.6)
14. Shorten L in increments of 20.0 cm and measure T
for each length.
15. Repeat the procedure using the wood ball.
16. Produce graphs of T2
vs. L for each ball. Apply a
linear fit; print a copy for each partner.
QUESTIONS
1. Solve Eq. 11.3 for g.
2. Does the period of a simple pendulum depend on
the mass?
3. How long must a simple pendulum be to have a
period of 1.5 s?
4. Assume you are safely located on the moon and have
access to a simple pendulum, stopwatch, and meter
stick. Is it possible to determine the acceleration
due to gravity of the moon, gmoon, using only these
three items? (Hint: gmoon 6= 0 m/s2
)
5. Consider your T2
vs. L graph. What are the slope
values? Show that the slope should be equal to
4⇡2
/g. Compare each graph value to the accepted
value.