Question

The bob of a simple pendulum is released at time t = 0 from a position of small angular displacement. Its linear displacement is ______.

(l = length of simple pendulum and g = acceleration due to gravity, A = amplitude of S.H.M.)

Options

• `A sin (sqrt(l/g))t`

• `A cos (sqrt(g/l))t`

• `A sin (sqrt(g/l))t`

• `A cos (sqrt(l/g))t`

Answer 1

The bob of a simple pendulum is released at time t = 0 from a position of small angular displacement. Its linear displacement is `underline(A cos (sqrt(g/l))t)`.

Explanation:

Equation of SHM

x = A cos ωt where ω = `[becauseT=2pisqrt(l/g)   thereforeomega=(2pi)/(2pisqrt(l/g))=sqrt(g/l)]`

`x=Acossqrt(g/l)t`