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?

The answer is "F ↔ x".

The magnitude of F is directly proportional to the magnitude of X. It is when the harmonic simple harmonic motion undergo. In physics simple harmonic motion is the motion where restoring force is directly proportional to the displacements. The direction is also opposite to the displacement.