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Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS...

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Chapter 13 Oscillations About Equilibrium
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Page 1: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Chapter 13 Oscillations About Equilibrium

Page 2: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

FOCUSED LEARNING TARGETGIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM , I WILL BE ABLE TO CALCULATE FORCE OF SPRING (FS) , TOTAL ENERGY IN TERMS OF ELASTIC POTENTIAL ENERGY (US) AND KINETIC ENERGY (K), FREQUENCY (f) AND PERIOD (t) USING THE FOLLOWING EQUATIONS FS = -kx ; K= ½ mv2 ; Ki + Ui = Kf +Uf

US = ½ kx2= ½ kA2 ; E = K + U ; T= 1/f ; f = 1/T

f = 1/2π √k/m ; T = 2π√m/k ; vmax = A√k/m

Page 3: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

HOMEWORK :

• CHAPTER 13. 1- 13.7 SUMMARIES • 1 EXAMPLE FOR EACH SECTION• 2 HW PROBLEMS(ODD ) FOR EACH SECTION • 2 PROBLEMS IN THE COLLEGE BOARD•

https://apstudent.collegeboard.org/apcourse/ap-physics-b/exam-practice

Page 4: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Experiment :PENDULUM

1. HYPOTHESIS :

WHAT WILL HAPPEN TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE MASS OF THE PENDULUM INCREASES?

________________

2. HYPOTHESIS :

WHAT WILL HAPPEN TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE STRING OF THE PENDULUM INCREASES?

________________

Page 5: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW :PendulumPart 1:Half of the String’s Length

3. Length of the String _______cm

4. How many complete cycles in one minute ? Do

3 trials and get the average

Cycles = _______

Time = 1 minute

5. Frequency in cycles per minute = ___________

6.Frequency in cycles per second =_____________7. Period =_____sec

Page 6: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

PendulumPart 2 : Double the Length of the String

8. Length of the String _______cm

9. How many complete cycles in one minute ? Do

3 trials and get the average

Cycles = ______

Time = 1 minute

10. Frequency in cycles per minute = ___________

11.Frequency in cycles per second =_____________12. Period = ________sec

Page 7: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

PendulumPart 3 : Double the Mass and Use Half of the String’s Length

13. Length of the String _______cm14. How many complete cycles in one minute ? Do 3 trials and get the average Cycles = ______Time = 1 minute

15. Frequency in cycles per minute

= ___________

16.Frequency in cycles per second

=_____________

17. Period = ____sec

Page 8: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Conclusion

15. WHAT HAPPENS TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE STRING OF THE PENDULUM INCREASES?

16. WHAT HAPPENS TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE MASS OF THE PENDULUM INCREASES?

Page 9: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Read p 444-446

Vocabulary :1. Oscillation2. Propagation3. Wave pulse 4. Hooke’s Law5. Simple Harmonic

Motion6. Displacement 7. Amplitude

8. Period9. Frequency 10. HertzEquations Necessary :

Page 10: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

1. Periodic Motion

• Motion that repeats itself over a fixed and reproducible period of time.

• The revolution of a planet about its sun is an example of periodic motion. The highly reproducible period (T) of a planet is also called its year.

Page 11: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 2. Mechanical devices on earth can be designed to have periodic motion. These devices are useful timers. They are called oscillators.

Page 12: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

3. Simple Harmonic Motion You attach a weight to a spring, stretch the spring past

its equilibrium point and release it. The weight bobs up and down with a reproducible period, T.

• Plot position vs. time to get a graph that resembles a sine or cosine function. The graph is "sinusoidal", so the motion is referred to as simple harmonic motion.

• Springs and pendulums undergo simple harmonic motion and are referred to as simple harmonic oscillators.

Page 13: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 14: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 15: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

4. Crest5. Troughs6. Amplitude- Maximum displacement from equilibrium. Related to energy. 7. Equilibrium

Page 16: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

7. Period(T)

Length of time required for one oscillation.

Page 17: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

8. Frequency

• How fast the oscillator is oscillating. • f = 1/T • Unit: Hz or s-1

Page 18: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

9. Springs

Springs are a common type of simple harmonic oscillator.

Our springs are "ideal springs", which means • They are massless. • They are both compressible and extensible. They will follow Hooke's Law. • Fs = -kx

Page 19: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 20: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

11. F=-kx ( Fs opposite with X)

FS= 0

FS

FS

X > 0

X< 0

Page 21: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

12.Fs = -kx

The acceleration of the block is equal to a = Fs / m

13.Another way to describe the block’s motion is the energy it transfers.

Us = ½ k x2

When you pull the block, you are increasing the elastic potential energy.

Page 22: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

14. Releasing the block , potential energy becomes kinetic energy as the block moves. As it passes through equilibrium Us =0 , so all energy is K.

15. As it passes again through equilibrium , it compresses the spring , K –kinetic becomes Us- elastic potential

Page 23: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

11. F=-kx ( Fs opposite with X)

FS= 0

FS

FS

X > 0

X< 0

Us =maximized

Us =maximized

K is maximizedUs = 0

K =0V=0

K =0V=0

Page 24: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 13. A 12 cm long spring has a force constant (k) of 400 N/m . How much force is required to stretch the spring to a length of 14cm.

Page 25: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 13. A 12 cm long spring has a force constant (k) of 400 N/m . How much force is required to stretch the spring to a length of 14cm.

• F = -kx• F = - 400N/m ( .14m -.12m) = - 8 N

Page 26: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Conservation of EnergySprings and pendulums obey conservation of

energy. • The equilibrium position has high kinetic

energy and low potential energy. • The positions of maximum displacement have

high potential energy and low kinetic energy. • Total energy of the oscillating system is

constant.

Page 27: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

14. A block of mass m = 2 kg is attached to an ideal spring of force constant k = 500N/m . The amplitude of the resulting oscillations is 8 cm . Determine the total energy of the oscillator and the speed of the block when it is 4 cm from equilibrium.

Page 28: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

14. A block of mass m = 2 kg is attached to an ideal spring of force constant k = 500N/m . The amplitude of the resulting oscillations is 8 cm . Determine the total energy of the oscillator and the speed of the block when it is 4 cm from equilibrium. E = Us + K = ½ kx2 + 0 = ½ (500N/m)(.08m)2 =1.6J1.6J= ½ kx2 + ½ mv2 = ½ (500N/m)(.04m)2 + ½ (2kg) v2

v = 1.1 m/s

Page 29: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

14. A block of mass m = 0.05 kg oscillates on a spring whose force constant k is 500 N/m. The amplitude of the oscillations is 4 cm . Calculate the maximum speed of the block .

Page 30: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

14. A block of mass m = 0.05 kg oscillates on a spring whose force constant k is 500 N/m. The amplitude of the oscillations is 4 cm . Calculate the maximum speed of the block . Us = ½ kx2 K = ½ mv2

½ kx2 = ½ mv2 v = √ kX2 /m v =√ 500N/m ( .04m)2/ 0.05kg v = 4m/s

Page 31: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

15. A block of mass m = 8kg is attached to an ideal spring of force constant k = 500N/m . The block is at rest at its equilibrium position. An impulsive force acts on a block , giving it an initial speed of 2m/s . Find the amplitude of the resulting oscillations?

Page 32: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

15. A block of mass m = 8kg is attached to an ideal spring of force constant k = 500N/m . The block is at rest at its equilibrium position. An impulsive force acts on a block , giving it an initial speed of 2m/s . Find the amplitude of the resulting oscillations? Ei = Ef Ki + Ui = Kf + Uf ½ mv2 + 0 = 0 + ½ kx2

8kg (2m/s)2= 500N/m X2

x = 0.25 m

Page 33: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW :

• A mass of 0.5 kg is connected to a massless spring with a force constant k of 50N/m . The system is oscillating on a frictionless horizontal surface . If the amplitude of the oscillations is 2cm , what is the total energy of the system ?

Page 34: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 16. A block oscillating on the end of a spring moves from its position of a maximum spring stretch to maximum spring compression in 0.25sec . Determine the period and frequency of this motion.

Page 35: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 16. A block oscillating on the end of a spring moves from its position of a maximum spring stretch to maximum spring compression in 0.25sec . Determine the period and frequency of this motion.

Page 36: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 16. A block oscillating on the end of a spring moves from its position of a maximum spring stretch to maximum spring compression in 0.25sec . Determine the period and frequency of this motion.

• For whole cycle T = 0.5sec • f = 1/T = 1/0.5s = 2 Hertz

Page 37: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW:

. A student observing an oscillating block counts 45.5 cycles of oscillations in one minute . Determine its frequency in hertz and period in seconds.

Page 38: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW

. A student observing an oscillating block counts 45.5 cycles of oscillations in one minute . Determine its frequency in hertz and period in seconds. f= 45.5 cycles/min X 1min/60sec = 0.758 cycles/sec = 0.758 Hz T = 1/f = 1/ 0.758Hz= 1.32 sec

Page 39: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

17. A block of mass m = 2 kg is attached to a spring whose force constant k , is 300 N/m . Calculate the frequency and period of the oscillations of this spring –block system.

Page 40: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

17. A block of mass m = 2 kg is attached to a spring whose force constant k , is 300 N/m . Calculate the frequency and period of the oscillations of this spring –block system. f = 1/2π √k/m f = 1/2π√ (300N/m) / 2kg f = 1.9 Hz T = 1/f = 1/ 1.9Hz = 0.51 sec

Page 41: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 18. A block is attached to a spring and set into oscillatory motion and its frequency is measured . If this block were removed and replaced by a second block with ¼ the mass of the first block , how would the frequency of the oscillations compare to the first block ?

Page 42: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

• 18. A block is attached to a spring and set into oscillatory motion and its frequency is measured . If this block were removed and replaced by a second block with ¼ the mass of the first block , how would the frequency of the oscillations compare to the first block ?

f = 1/2π √ k/m = 1/2π √ k / (1/4)m f = 1/2π√ 4k/m = 1/2π (2) √k/m f increased by a factor of 2

Page 43: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 44: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW: Calculate the period of a 300-g mass

attached to an ideal spring with a force constant of 25 N/m.

Page 45: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW A 300-g mass attached to a spring

undergoes simple harmonic motion with a frequency of 25 Hz. What is the force constant of the spring?

Page 46: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW : An 80-g mass attached to a spring hung vertically causes it to stretch 30 cm from its unstretched position. If the mass is set into oscillation on the end of the spring, what will be the period?

Page 47: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 48: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 49: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 50: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Sample Problem You wish to double the force

constant of a spring. You • A. Double its length by connecting

it to another one just like it. • B. Cut it in half.• C. Add twice as much mass.• D. Take half of the mass off.

Page 51: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Sample Problem You wish to double the force

constant of a spring. You • A. Double its length by connecting

it to another one just like it. • B. Cut it in half.• C. Add twice as much mass.• D. Take half of the mass off.

Page 52: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

CW : Sample problem. A 2.0-kg mass attached to a spring oscillates with an

amplitude of 12.0 cm and a frequency of 3.0 Hz. What is its total energy?

Page 53: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 54: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

19. Pendulums A simple pendulum consists of a weight of mass

m attached to a string or a massless rod that swings without friction, about the vertical equilibrium position .

The pendulum can be thought of as a simple harmonic oscillator.

The displacement needs to be small for it to work properly.

Page 55: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 56: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.
Page 57: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

21. RESTORING FORCE

• FRESTORING = mg Sinθ• The restoring force is provided by gravity.• Displacement is zero at equilibrium.• At the endpoints of the oscillation region , the

restoring force and tangential acceleration at have the greatest magnitudes, the speed of the pendulum is zero , potential energy is maximized.

• As the pendulum passes through the equilibrium position, its kinetic energyand speed are maximized.

Page 58: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

22. A simple pendulum has a period of 1s on earth. What would be its period on the Moon( where g = 1/6 of the earth )

T= 2π√ L/g T = increased by √6 = 1sec X √6

Page 59: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Sample problem Predict the period of a pendulum consisting of a 500

gram mass attached to a 2.5-m long string.

Page 60: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Sample problem Suppose you notice that a 5-kg weight tied to a string

swings back and forth 5 times in 20 seconds. How long is the string?

Page 61: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Sample problem The period of a pendulum is observed to be T.

Suppose you want to make the period 2T. What do you do to the pendulum?

Page 62: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

Conservation of EnergyPendulums also obey conservation of energy. • The equilibrium position has high kinetic

energy and low potential energy. • The positions of maximum displacement have

high potential energy and low kinetic energy. • Total energy of the oscillating system is

constant.

Page 63: Chapter 13 Oscillations About Equilibrium. FOCUSED LEARNING TARGET GIVEN VIBRATIONS AND OSCILLATIONS CAUSED BY SPRING AND PENDULUM, I WILL BE ABLE TO.

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