Oscillations · Question 59

The bob of simple pendulum having length l, is displaced from mean position to an angular position with respect to vertical. If it is released, then velocity of bob at equilibrium position

1. 2gl(1 - )
2. 2gl(1 + )
3. 2gl
4. 2gl

Answer

(1) 2gl(1 - )

Solution

When the bob is at angle , its height above the mean (lowest) position is:

h = l - l = l(1 - )

By conservation of mechanical energy (released from rest):

12mv2 = mgh = mgl(1 - )

v = 2gl(1 - )

Answer: (1)