Answer the following with reference to a simple pendulum executing small-amplitude oscillations under gravity.
(i) Define a simple pendulum.
(ii) List any three assumptions made while analysing its motion for small oscillations.
(iii) Write the expression for the tangential restoring force acting on the bob in terms of arc-length displacement s.
(iv) State the corresponding differential equation of motion for the bob and identify the quantity that represents the angular frequency.
(v) Write the formula for the time period T of the pendulum in terms of its length L and the acceleration due to gravity g.