A student says that he had applied a force F = k√x on a particle and

1.	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.
Answer» (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.

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.

Answer»

(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.