First slide

Simple harmonic motion

Question

The amplitude of a particle executing SHM is made three-fourth keeping its time period constant. Its total energy will be

Moderate

A

$\frac{E}{2}$
B

$\frac{3}{4} E$
C

$\frac{9}{16} E$
D

None of these

Solution

$E = \frac{1}{2} {mω}^{2} a^{2}$ $\Rightarrow \frac{E^{'}}{E} = \frac{{a^{'}}^{2}}{a^{2}}$ $\Rightarrow \frac{E^{'}}{E} = \frac{{(\frac{3}{4} a)}^{2}}{a^{2}}$ $(∵ a^{'} = \frac{3}{4} a)$
$\Rightarrow E^{'} = \frac{9}{16} E$

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