Ch. 14 Outline

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Ch. 14 Outline

• Ideal Spring creates Simple Harmonic Motion
  (SHM)
• SHM is an oscillation which is sinusoidal in
  time
• Amplitude is the size of the oscillation
• Frequency depends on spring-strength to mass
  ratio
• Frequency does not depend on amplitude
• Mechanical Energy does depend on amplitude

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Main Results
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Ideal Spring and SHM
Obeys Hookes Law F -kx
Any object acted on solely by an Ideal Spring
undergoes Simple Harmonic Motion (SHM)
Any object acted on by a restoring net-force that
is proportional to displacement undergoes Simple
Harmonic Motion (SHM)
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A Amplitude (m) T Period (s)
T
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• angular frequency (rad/s)
• f frequency (Hz)
• 2pf
• f w/2p

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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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Energy in SimpleHarmonic Motion
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Etotal U K
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Some Oscillating Systems
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Summary

• Ideal Spring creates Simple Harmonic Motion
  (SHM)
• SHM is sinusoidal in time
• Frequency depends on spring-strength to mass
  ratio
• Frequency does not depend on amplitude
• Mechanical Energy does depend on amplitude

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Damped Oscillations
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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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