Show that the steady state complex amplitude of a damped oscillator driven by an external force F exp (iwt) is given by the expression

Explain the meanings of the symbols used and the condition for resonance. A machine of total mass 100 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 damping constant of 942 Ns m?1. The machine contains an eccentrically mounted shaft which, when rotating at an angular frequency w, produces a vertical force on the system of F0w2 cos wt, where F0 is constant. It is found that resonance occurs at 1200r.p.m. (revolutions per minute) and the amplitude of vibration in the steady state is then 1 cm. Estimate the amplitude of vibration in the steady state when the driving frequency is

(a) 2400 r.p.m and

(b) Very large. You may assume that gravity has a negligible effect on the motion.

Transcribed Image Text:

M(u - u) + iwb