Sunday, February 5, 2012

How to find distance with Simple harmonic motion?

A mass moves back and forth in simple harmonic motion with amplitude A and period T.

(a) In terms of A, through what distance does the mass move in the time T?

(b) In terms of A, through what distance does it move in the time 4.75T?How to find distance with Simple harmonic motion?the amplitude is the maximum distance from the equilibrium point; so let's imagine the mass starts all the way at one extreme point, a distance A from equilibrium, the mass will go through equilibrium to the farthest point on the other side, and return to its starting point



the farthest point on the other side of the equilibrium point is A units on the other side, so the mass travels 2 A units to get to the far side, and 2A units to return, for a total of 4A units in one cycle



in 4.75 cycles, the total distance is simply 4x4.75A=19A
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