A machine part of mass 2kg is attached to a vertical spring of force constant 800Nm−1. The part is driven by a motor that applies a periodic force once every revolution of the motor shaft.
(i) Find the natural angular frequency and the natural frequency in hertz of the mass–spring system for small oscillations.
(ii) Determine the speed in revolutions per minute at which the motor is expected to cause resonance of the system.
(iii) After the system has been vibrating steadily at the speed found in part (ii), the motor is suddenly switched off. Explain qualitatively how and why the amplitude of oscillation will vary with time thereafter.