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_lec34_ppt_ - Lecture 34 P112 Agenda for today New Subject...

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Lecture 34 Apr 16, 2006 P112
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Agenda for today ± New Subject: Simple Harmonic Motion
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Simple Harmonic Motion (SHM) ± We know that if we stretch a spring with a mass on the end and let it go, the mass will oscillate back and forth (if there is no friction). ± This oscillation is called Simple Harmonic Motion , and is actually very easy to understand... k m k m k m
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How the spring oscillator works ± You extend the spring and let it go ± The spring force and acceleration are to the left, so the speed increases as it approaches the equilibrium position ± The net force at that point is zero, but it overshoots the equilibrium position and compresses the spring ± At that point the process start over again.
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SHM Dynamics ± At any given instant we know that F = m a must be true. ± But in this case F = -kx ± SO: k x m F = -kx a a differential equation for x(t) ! d 2 x dt 2 = ± k m x ± kx = ma = m d 2 x dt 2
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SHM Dynamics... Try the solution x = A cos( ± t) This works, so it must be a solution!
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