Physics - SHM Question with Solution | TestHub

From the given displacement-time graph, the displacement $y$ of the particle at time $t$ starts from the origin and initially increases in the positive direction. This can be represented by the equation:

$y=A\sin (\omega t)$

where $A$ is the amplitude and $\omega$ is the angular frequency.

For a particle performing simple harmonic motion, the restoring force $F$ is directly proportional to the negative of the displacement:

$F=-ky$

where $k$ is the force constant.

Substituting the expression for $y$, we get:

$F=-k(A\sin (\omega t))=-kA\sin (\omega t)$

This equation indicates that the force-time graph is a sine wave with a negative amplitude. It starts from zero at $t=0$ and initially goes in the negative direction.

Comparing this with the given options, graph (c) correctly represents this relation.

Answer: c