Question

The bob in a simple pendulum of length $\ell$ is released at $t=0$ from the position of small angular displacement $\theta$. Linear displacement of the bob at any time $t$ from the mean position is given by

• A. $\ell \theta \cos \sqrt{\frac{g}{l}}t$
• B. $\ell \sqrt{\frac{g}{l}}t\cos \theta$
• C. $\ell g\sin \theta$
• D. $\ell \theta \sin \sqrt{\frac{g}{l}}t$

Answer 1

The correct option is B $\ell \sqrt{\frac{g}{l}}t\cos \theta$

$x=l\cos wt$

$=l\sqrt{\frac{g}{L}}t\cos \theta$