According to the textbook, 'Every periodic motion is not simple harmonic motion. Only that periodic motion governed by the force law F = -kx is simple harmonic.' The force in SHM must be proportional to displacement and directed towards the centre of motion. For (a), Earth's rotation is uniform circular motion without any restoring force - hence periodic but not SHM. For (b), the mercury column experiences a restoring force proportional to displacement (due to pressure difference from height difference), making it SHM. For (c), the textbook states 'The motion of a simple pendulum is simple harmonic for small angular displacement' - a ball bearing in a smooth bowl behaves similarly to a pendulum for small displacements. For (d), general vibrations of a polyatomic molecule are complex multi-mode oscillations that don't strictly follow F = -kx.