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Saturday, December 13, 2008

Q) A particle starts from rest x=0 at t=0, moves on a straight-line path and again comes to rest at x=1 at t=1. If the motion is simple harmonic, find the approx. maximum acceleration.

A) Using apt equations of simple harmonic motion:
x = A.cos(wt)
(since the abcissa 1/2 is the midpoint of the given path, we measure amplitude and displacement by considering that as the central point)

At t=1 ---> 1/2 = 1/2* cos (w)
so, w = pi

And since acceleration (a) = -w^2. x
magnitude of a = (pi^2). (1/2) (a is max. at extremities)
= approx 5 units/s^2
--------> max. magnitude of acceleration

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