A restoring force of magnitude F acts on a system with a displacement of magnitude x. In which of the following cases will the system undergo simple harmonic motion?

a. F∝ √ x
b. F ∝ Sinx
c. F ∝ x^2
d. F ∝ x
e. F ∝1/x

Option (d)

Explanation:

The above mathematical expression for the force F and displacement x is a statement of Hooke's law.

The simplest kind of oscillation occurs when the restoring force F is directly proportional to the displacement x. Systems that obey hooke's law such as an ideal stretched spring with a load attached to it undergo simple harmonic motion. The constant of proportionality is k having the units of N/m and

F = kx

The displacement x is the displacement of the spring from equilibrium position.

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