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 constant or not. Assume that he has worked only with positive x and no other force acted on the particle

Question

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 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 and k remains constant (D) the motion cannot be simple harmonic

Tardigrade Admin · Accepted Answer

It is given that F=-k√x But For SHM F=-k0x Therefore by comparing them k=k0√x Therefore as x increases k increases

Q. 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 constant or not. Assume that he has worked only with positive $x$ and no other force acted on the particle

as $x$ increases $k$ increases

as $x$ increases $k$ decreases

as $x$ increases and $k$ remains constant

the motion cannot be simple harmonic

It is given that $F = - k x$
But For SHM $F = - k_{0} x$
Therefore by comparing them $k = k_{0} x$
Therefore as $x$ increases $k$ increases

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

as x increases k increases

as x increases k decreases

as x increases and k remains constant