PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A point mass m is suspended by a light, inextensible string of length l to form a simple pendulum.
(i) Starting from the restoring torque acting on the bob when it is displaced through a small angle θ, derive the differential equation governing its angular motion.
(ii) Hence obtain an expression for the time period of small oscillations of the pendulum.
(iii) Using your result, calculate the time period of a pendulum of length 0.75 m at a place where the acceleration due to gravity is 9.8 m s−2. Express your answer to two significant figures.