Consider a simple pendulum of length L and bob mass m displaced slightly from its equilibrium position.
(a) Resolve the weight of the bob into components and, neglecting air resistance, derive an expression for the tangential restoring force in terms of m, g and the angular displacement θ (in radians).
(b) Express this restoring force in terms of the arc–length displacement s and hence obtain the differential equation governing the motion of the pendulum in s.
(c) Show that the resulting motion is simple harmonic and obtain an expression for the angular frequency ω.