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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. ... – PowerPoint PPT presentation

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Title: 14 Oscillations and Waves


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
    Hookes Law (F -kx).

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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 occurs at center of motion v 0 at
turnaround points (x A)
vmax wA
7
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
21
Resonance Time dependent force transmits large
amounts of energy to an oscillating object at the
natural frequency.
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