A simple pendulum consists of a small bob attached to a light inextensible string of…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A simple pendulum consists of a small bob attached to a light inextensible string of length L. The bob is given a small initial displacement and released.
(i) Define the term "restoring force" with reference to this situation.
(ii) Explain with the aid of a labelled diagram why the restoring force on the bob is always directed towards the mean position.
(iii) Show geometrically that the arc–length displacement s of the bob from the mean position is related to the angular displacement θ (in radians) by s=Lθ when the arc is part of a circle of radius L.
(iv) Using qualitative reasoning only, describe why the motion of the pendulum may be treated as simple harmonic for small values of θ.