First slide

Simple hormonic motion

Question

The angular velocity and amplitude of a simple pendulum are ‘ $ω$ ’ and A respectively. At a displacement ‘x’. If its KE is ‘T’ and PE is ‘U’ then the ratio of 'T' to ‘U’ is

Easy

A

$\large \frac{{{x^2}{w^2}}}{{{A^2} - {w^2}{x^2}}}$
B

$\large \frac{{{x^2}}}{{{A^2} - {x^2}}}$
C

$\large \frac{{{A^2} - {w^2}{x^2}}}{{{x^2}{w^2}}}$
D

$\large \frac{{{A^2} - {x^2}}}{{{x^2}}}$

Solution

$\large K.E\, = \,\frac{1}{2}m{\omega ^2}\left( {{A^2} - {x^2}} \right)\, = \,T;$
$\large P.E\, = \,\frac{1}{2}m{\omega ^2}{x^2} = \,U;$
$\large \frac{T}{U}\, = \,\frac{{\frac{1}{2}m{\omega ^2}\left( {{A^2} - {x^2}} \right)}}{{\frac{1}{2}m{\omega ^2}{x^2}}}\, = \,\frac{{{A^2} - {x^2}}}{{{x^2}}}$

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