A particle of mass m moves in one dimension and is subject to a restoring force which is proportional to its displacement x and a damping force which is proportional to its velocity. Derive the differential equation for its motion when it is also acted upon by a driving force F0 cos wFt. If x = A cos (wFt + Φ), show that at low frequencies wF the phase Φ is zero and the amplitude A is independent of the driving frequency wF, whereas at high frequencies Φ = π and A depends on wF.