A simple pendulum of length $L$ and mass (bob) $M$ is oscillating in a plane about a vertical line between angular limits $-\mathrm{\varphi } \mathrm{and} \mathrm{\varphi }$. For an angular displacement $\mathrm{\theta }, [\left|\mathrm{\theta }\right| < \mathrm{\varphi }]$ the tension in the string and velocity of the bob are $T$ and $v$, respectively. The following relations hold good under the above conditions