A simple pendulum of length and bob mass executes small angular oscillations in a…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A simple pendulum of length L and bob mass m executes small angular oscillations in a vertical plane. Air resistance produces a damping torque −cdtdθ about the point of suspension, while a periodic driving torque τ0sinωdt is applied at the support.
(i) Write expressions for (a) the restoring torque and (b) the damping torque acting on the bob when its angular displacement is θ.
(ii) Using these torques and the equation of rotational motion, derive the differential equation governing θ(t).
(iii) Show that the equation in part (ii) reduces to appropriate simpler forms when (a) the damping torque is absent and (b) the driving torque is absent.
(iv) For case (a) of part (iii), obtain the natural angular frequency of small oscillations of the pendulum.