1. Chapter 13
Oscillatory Motion

2. Periodic motion Periodic (harmonic) motion – self-repeating motion
Oscillation – periodic motion in certain direction
Period (T) – a time duration of one oscillation
Frequency (f) – the number of oscillations per unit time, SI unit of frequency 1/s = Hz (Hertz)
Heinrich Hertz
( )

3. Simple harmonic motion
Simple harmonic motion – motion that repeats itself and the displacement is a sinusoidal function of time

4. Amplitude
Amplitude – the magnitude of the maximum displacement (in either direction)

5. Phase

6. Phase constant

7. Angular frequency

8. Period

9. Velocity of simple harmonic motion

10. Acceleration of simple harmonic motion

11. Chapter 13
Problem 19
Write expressions for simple harmonic motion (a) with amplitude 10 cm, frequency 5.0 Hz, and maximum displacement at t = 0, and (b) with amplitude 2.5 cm, angular frequency 5.0 s-1, and maximum velocity at t = 0.

12. The force law for simple harmonic motion
From the Newton’s Second Law:
For simple harmonic motion, the force is proportional to the displacement
Hooke’s law:

13. Energy in simple harmonic motion
Potential energy of a spring:
Kinetic energy of a mass:

14. Energy in simple harmonic motion

15. Energy in simple harmonic motion

16. Chapter 13
Problem 34
A 450-g mass on a spring is oscillating at 1.2 Hz, with total energy 0.51 J. What’s the oscillation amplitude?

17. Pendulums Simple pendulum: Restoring torque:
From the Newton’s Second Law:
For small angles

18. Pendulums
Simple pendulum:
On the other hand

19. Pendulums
Simple pendulum:

20. Pendulums
Physical pendulum:

21. Chapter 13
Problem 28
How long should you make a simple pendulum so its period is (a) 200 ms, (b) 5.0 s, and (c) 2.0 min?

22. Simple harmonic motion and uniform circular motion
Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

23. Simple harmonic motion and uniform circular motion
Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

24. Simple harmonic motion and uniform circular motion
Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

25. Simple harmonic motion and uniform circular motion
Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the circular motion occurs

26. Damped simple harmonic motion
Damping
force
Damping
constant

27. Forced oscillations and resonance
Swinging without outside help – free oscillations
Swinging with outside help – forced oscillations
If ωd is a frequency of a driving force, then forced oscillations can be described by:
Resonance:

28. Questions?

29. Answers to the even-numbered problems
Chapter 13
Problem 20
0.15 Hz; 6.7 s

30. Answers to the even-numbered problems
Chapter 13
Problem 38
65.8%; 76.4%