(a) Starting from the tangential component of the weight of a pendulum bob, write the…
PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
(a) Starting from the tangential component of the weight of a pendulum bob, write the restoring force when the bob is displaced through an angle θ from the vertical.
(b) Explain clearly why the force obtained in part (a) can be treated as that of simple harmonic motion only for very small angular displacements. State the quantitative limit (in degrees) that is commonly accepted for this purpose.
(c) Describe qualitatively how, and in which direction (increase or decrease), the time period of a pendulum would change if the initial angular amplitude is gradually increased from 5∘ to 20∘, keeping the length unchanged.
(d) Give two practical precautions that a student must follow in a laboratory experiment to ensure that the motion of a simple pendulum remains within the small-angle regime.