A ball of mass m suspended by a weightless spring can perform vertical oscillations with damping coefficient β. The natural oscillation frequency is equal to ω0. Due to the external vertical force varying as F = F0 cos ωt the ball performs steady-state harmonic oscillations. Find:
(a) the mean power (P), developed by the force F, averaged over one oscillation period;
(b) the frequency ω of the force F at which (P) is maximum; what is (P)max equal to?