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Unformatted text preview: mx2 + 1 kx2 by straightforward diﬀerentiation (getting a simple result in terms of x, x, and/or x) and
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then with the help of Taylor 5.24, show that it is exactly minus the rate at which energy is dissipated
by Fdamp .
The rest is pure extra credit, worth up to 6 points!
The position of an overdamped oscillator is given by Eq. 5.40 in Taylor’s text. Find the constants C1 and
C2 in terms of the initial position x0 and velocity v0 . Then, sketch the behavior of x(t) for the two separate
cases x0 = 0, and v0 = 0. Finally, show that if you let β = 0, your solution for x(t) matches the correct
solution for undamped motion.
(I ﬁnd this rather remarkable, since the solution you started from is for the overdamped case, it wasn’t
supposed to work for the undamped case?!) As Taylor puts it, the math is sometimes cleverer than we are!...
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This document was uploaded on 03/09/2014 for the course PHYSICS 2210 at Colorado.
 Spring '11
 STEVEPOLLOCK
 mechanics, Work

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