Question

A mass moves back and forth in simple harmonic motion with amplitude A and period T. (a) In terms of the period, how much time does it take for the mass to move through a total distance 2A

Answer 1

A mass moves back and forth in simple harmonic motion with amplitude A and period T. (a) In terms of the period, it will take T/2 time for the mass to move through a total distance 2A

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position.

Total distance covered by the mass

This is so because in one cycle, the mass moves from

x=A to x=0,

then from x=0 to  x=−A

then x= −A  to x=0

and back from =0 to x=A.

Total distance covered in time period T will be = |A| + |-A| +|-A| + |A|

                                                                              = 4A

Since , 4A distance is covered in time period = T

2A distance will get covered in a time period of = T/2

To learn more about simple harmonic motion here

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