Question

The bob in a simple pendulum of length $\phi$ is released at t = 0 from the position of small angular displacement ${\theta }_0$. Linear displacement of the bob at any time t from the mean position is given by

• A. $\phi {\theta }_0\cos \sqrt{\frac{g}{\phi }}t$
• B. $\phi \sqrt{\frac{g}{\phi }}t\cos {\theta }_0$
• C. $\phi g\sin {\theta }_0$
• D. $\phi {\theta }_0\sin \sqrt{\frac{g}{\phi }}t$

Answer 1

The correct option is A $\phi {\theta }_0\cos \sqrt{\frac{g}{\phi }}t$

Length of pendulum $=\phi$

Maximum angular displacement$={\theta }_0$ (as it is released from this angle )

Corresponding maximum linear displacement, i.e.,amplitude$=\phi {\theta }_0$.

As the bob is released from extreme position so the linear displacement at any time $x=\phi {\theta }_0\cos \sqrt{\frac{g}{\phi }}t$

Where angular frequency of oscillation is given by, $\omega =\sqrt{\frac{g}{\phi }}$