The angular velocity and the amplitude of a simple pendulum is $\omega $ and $a$ respectively. At a displacement $X$ from the mean position if its kinetic energy is $T$ and potential energy is $V$, then the ratio of $T$ to $V$ is
AIPMT 1991, Medium
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(d) Kinetic energy $T = \frac{1}{2}m{\omega ^2}({a^2} - {x^2})$
and potential energy, $V = \frac{1}{2}m{\omega ^2}{x^2}$
and potential energy, $V = \frac{1}{2}m{\omega ^2}{x^2}$
$\therefore \frac{T}{V} = \frac{{{a^2} - {x^2}}}{{{x^2}}}$
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