Can simple harmonic motion take place in a non-inertial frame? If yes, should the ratio of the force applied with the displacement be constant?
Yes, simple harmonic motion can take place in a non-inertial frame also. But we have to apply pseudo force to maintain the body in S.H.M. The ratio of the force applied with the displacement will not be constant though. It is because the non-inertial frame of reference has its own acceleration with respect to the inertial frame of reference.