Question

A body is moving in a room with a velocity of 20 m/s perpendicular to the two walls separated by 5 meters. There is no friction and the collisions with the walls are elastic, the motion of the body
(1) Not periodic
(2) Periodic but not simple harmonic
(3) Periodic and simple harmonic
(4) periodic with variable time period
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☆Explain the answer briefly.
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Answer 1

Answer:

(2) Periodic but not Simple Harmonic.

Explanation:

If a body keeps performing the same cyclic movement, e.g. moving between two points A and B with a constant period (A to B and back to A), the motion is called periodic.

SHM, whereas, is a special type of periodic motion where the acceleration is proportional to the displacement from the mean position.

The body bounces, elastically, backwards and forwards and the period is constant [(5+5/20) = 0.5s for each cycle]. Hence, the motion is clearly periodic.

Also, there is no change in energy of the body, that means no external force acts upon it and it in turn implies that there is no acceleration, so it’s motion is not Simple Harmonic.

The option that suits all the conclusions is (2) and hence the correct answer.