Question

If a simple pendulum of length l has maximum angular displacement θ, what would be the maximum K.E. of the bob?

Answer 1

In the Fig., OA is the position of rest of the simple pendulum of length l.

Let ∠AOB = θ

From B, draw BC ⊥ OA. In going from A to B,

the bob rises through a height AC, where

AC = OA - OC

= OA - OB cosθ = l - l cosθ

h = l (1 - cosθ)

P.E. acquired at B,

= mgh = mgl (1 - cosθ),

which would be the maximum K.E. on reaching A.