Question

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

• A. $\frac{ ( a^2 - x^2 \, \omega^2 ) }{ x^2 \, \omega^2 }$
• B. $\frac{ x^2 \, \omega^2}{ (a^2 - x^2 \, \omega^2 )}$
• C. $\frac{ (a^2 - x^2) }{ x^2 }$
• D. $\frac{ x^2 }{ (a^2 - x^2 )}$

Answer 1

Answer: (C)

$\frac{ (a^2 - x^2) }{ x^2 }$

Answer 2

PE. F = $\frac{1}{2} m \omega^2 \, x^2$
and KE, T = $\frac{1}{2} m \omega^2 (a^2 - x^2)$
$\therefore \frac{ T}{ V} = \frac{ a^2 - x^2 }{ x^2 }$