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

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

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

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

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

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

Etotal = U + K

Some Oscillating Systems

Formulas

Summary

Driven Oscillations and Resonance

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