(i) A simple pendulum consist of a small bob of mass m tied to a string of length L. Show that the total energy of oscillation of the pendulum is `E~=1/2 mg L theta_(0)^(2)` when it is oscillating with a small angular amplitude `theta_(0)`. Assume the gravitational potential energy to be zero of the lowest position of the bob. (ii) Three identical pendulums A, B and C are suspended from the ceiling of a room. They are swinging in semicircular arcs in vertical planes. The string of pendulum A snaps when it is vertical and it was found that the bob fell on the floor with speed `V_1`. The string of B breaks when it makes an angle of 30° to the vertical and the bob hits the floor with speed `V_2`. The string of pendulum C was cut when it was horizontal and the bob falls to the floor hitting it with a speed V3. Which is greatest and which is smallest among `V_1,V_2` and `V_3`?

Answer

(i) `V_(1)=V_(2)=V_(3)`