The motion of a simple pendulum executing S.H.M. is represented by following equation. $\mathrm{Y}=\mathrm{A} \sin (\pi \mathrm{t}+\phi)$, where time is measured in second. The length of pendulum is :

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Elasticity & SHM

The motion of a simple pendulum executing S.H.M. is represented by following equation.

Y = A sin (π t + ϕ)

, where time is measured in second.

The length of pendulum is :

Answer: (C)

Comparing with the standard SHM equation

y = A sin (ω t + ϕ)

, we get:

ω = π

rad/s

For a simple pendulum:

ω = \frac{g}{ℓ}

Therefore:

π = \frac{g}{ℓ}

Squaring:

π^{2} = \frac{g}{ℓ}

ℓ = \frac{g}{π ^{2}} = \frac{980}{π ^{2}} \approx \frac{980}{9.87} \approx 99.3

cm

Answer: (C) 99.4 cm

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Single correct option