A particle of mass m that is attached to a light spring is executing simple harmonic motion in a horizontal direction. State the condition relating to the net force acting on the particle that is necessary for it to execute simple harmonic motion.

Two steel balls, each of mass m, are welded to a light rod of length l and negligible mass and are initially at rest on a smooth horizontal surface. a horizontal force of magnitude f is suddenly applied to the rod as shown. determine (a) the instantaneous acceleration a of the mass center g and (b) the corresponding rate at which the angular velocity of the assembly about g is changing with time.