A student says that he had applied a force F = k√x on a particle and the particle moved in simple harmonic motion.

Monjur Alahi

A student says that he had applied a force F = k√x on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he has worked only with positive x and no other force acted on the particle.

(a) As x increases k increases.
(b) As x increases k decreases.
(c) As x increases k remains constant.
(d) The motion cannot be simple harmonic.


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Salim Ahmed Kawsar

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(a) As x increases k increases. 

Explanation:

Since the motion is simple harmonic, the force F=-⍵²x where ⍵² is a constant. Equating the force applied by the student we get, -k/x=-⍵²x 

→k=⍵²x² 

It is clear from this relation that if x increases k increases. 

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