A student investigates a simple pendulum consisting of a small bob of mass m suspended from a light, inextensible string of length L. The pendulum is displaced through a small initial angle θ0 and released from rest.
Throughout the experiment the student assumes the pendulum’s motion can be modeled as simple harmonic motion (SHM).
(a) Describe qualitatively how the torque acting on the bob depends on its angular displacement for small oscillations about the equilibrium position.
(b) Explain why the condition θ0≪1rad is necessary for the student’s SHM model to be valid.
(c) The student considers increasing the initial displacement to 25∘. Using reasoning based on the small-angle requirement, determine whether this larger displacement would still justify the SHM model, and clearly state your conclusion.
(d) If the SHM model remains valid, explain how the period of oscillation would change (if at all) when the amplitude is doubled. Justify your answer without performing a numerical calculation.