The bob of a simple pendulum of length L is displaced sideways through a small angle and released.
Answer the following questions with reasoning based on elementary geometry and the small–angle approximation.
(a) Establish the relation between the linear displacement s of the bob along the arc and the corresponding angular displacement θ of the string.
(b) Explain why the angle θ must be expressed in radians when using the relation obtained in part (a).
(c) State the range of angular amplitudes (in degrees) within which the small–angle approximation is considered valid for a simple pendulum and justify your answer.