1. 14 Oscillations and Waves
Simple Harmonic Motion
Energy in SHM
Some Oscillating Systems
Damped Oscillations
Hk: 31, 43, 49, 55, 59.

2. Oscillations
Simple Harmonic Motion: position varies sinusoidally with time, motion governed by Hooke’s Law (F = -kx).

4. A = Amplitude (m)
T = Period (s) T

5. Example: Object moves back and forth according to equation
x(t) = 3cos18t
Find w, f, and T.
w = 18 rad/s f = 18/2p = 9/p ~ 3 cycle/sec (cps)
T = 1/f = p/9 ~ 0.35 seconds/cycle

6. vmax = wA vmax occurs at center of motion
v = 0 at turnaround points (x = A)
vmax = wA

7. amax = Aw2 a = 0 at center of motion
amax occurs at turnaround points (x = A)
amax = Aw2

9. Etotal = U + K

12. Some Oscillating Systems

17. Formulas

18. Summary

20. Driven Oscillations and Resonance

21. Resonance:
Time dependent force transmits large amounts of energy to an oscillating object at the natural frequency.