14 Oscillations and Waves

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14 Oscillations and Waves

• Simple Harmonic Motion
• Energy in SHM
• Some Oscillating Systems
• Damped Oscillations
• Hk 31, 43, 49, 55, 59.

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Oscillations

• Simple Harmonic Motion position varies
  sinusoidally with time, motion governed by
  Hookes Law (F -kx).

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A Amplitude (m) T Period (s)
T
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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
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vmax occurs at center of motion v 0 at
turnaround points (x A)
vmax wA
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a 0 at center of motion amax occurs at
turnaround points (x A)
amax Aw2
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Etotal U K
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Some Oscillating Systems
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Formulas
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Summary
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Driven Oscillations and Resonance
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Resonance Time dependent force transmits large
amounts of energy to an oscillating object at the
natural frequency.
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