A machine of total mass 90 kg is supported by a spring resting on the floor and its motion is constrained to be in the vertical direction only. The system is lightly damped with a damping constant 900 Ns/m. The machine contains an eccentrically mounted shaft which, when rotating at an angular frequency p, produces a vertical force on the system of Fp2 sin pt where F is a constant. It is found that resonance occurs at 1200 r.p.m. (revolutions per minute) and the amplitude of vibration in the steady state is then 1 cm. Find the amplitude of vibration in the steady state when the driving frequency is (a) 2400 r.p.m. (b) 3000 r.p.m. (c) very large. Find also the quality factor Q at resonance. Assume that the gravity has a negligible effect on the motion.
