p140w07_ct_20 - Racquetball Striking a Wall Copyright:...

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Physics 140: Winter 2007 Lecture #20 March 21, 2007 Dave Winn Racquetball Striking a Wall Copyright: Loren M. Winters Mt. Etna Andrew Davidhazy
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Simple Harmonic Motion Review • Motion around stable equilibrium • Restoring force like Hooke’s law: F = -kx • Oscillations are harmonic x = Acos( ω t) ω = (k/m) • Energy in oscillations: trading elastic potential and kinetic energy – PE = 1/2kx 2 = 1/2kA 2 cos 2 ( ω t) – KE = 1/2mv 2 = 1/2m ω 2 A 2 sin 2 ( ω t)
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Consider a mass on a spring. Any real spring has some mass. When this mass is taken into account, what will happen to the period of oscillation of the spring/mass system? 1: The period will increase 2: The period will decrease 3: The period will remain the same The amount of restoring force remains the same, but the overall inertia is increase. This slows the oscillations.
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Imagine a mass which oscillates on an ideal massless spring. If I start the system moving with an amplitude A 0 , it oscillates with an angular frequency ω 0 . Now I start the system again, this time with an amplitude of 2A 0 . What is the angular frequency of oscillation now? 1: ω new = 2 ω 0 2: ω new = 4 ω 0 3: ω new = ω 0 4: ω new = ω 0 / 2 5: ω new = ω 0 / 4 Frequency of oscillation is unrelated to amplitude!
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Oscillations with friction… • Real oscillations eventually stop; energy is lost to friction • Oscillation amplitude gradually dies away as energy is drained off • Rate of fading depends on amount of friction, restoring force, and inertia
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One specific possibility… • If the friction depends on velocity
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This note was uploaded on 04/04/2008 for the course PHYSICS 140 taught by Professor Evrard during the Fall '07 term at University of Michigan.

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p140w07_ct_20 - Racquetball Striking a Wall Copyright:...

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