PHY354H1 Lecture Notes - Q Factor, Square Wave, Angular Velocity

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18 Jan 2014
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Lecture 12: varying the damping force, and adding sinusoidal driving forces. What does mean: at some point we made the variable change: = b/2m in our damped equations. At t = 0: x(0) = e0a = a. Remember the de nition of logarithmic decrement (where t is some multiple of the period). Since t is a multiple of the period: t = If we set t = 0 we get: x(t + t ) x(t) e (t+t ) e t x(t ) x(0) The time t when the amplitude has fallen to x(0)/e is therefore given by: e 1 = e t t = 1 = So physically, is the reciprocal of the time it takes for the amplitude to decay to e 1 of its original value. Its a measure of how fast the mechanical energy dissipates to thermal energy from friction. 1: notice that the units of are inverse seconds, the same units as 0.

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