First slide

Simple harmonic motion

Question

The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be

Moderate

A

18 J
B

10 J
C

12 J
D

2.5 J

Solution

$\frac{Potential energy (U)}{Total energy (E)} = \frac{\frac{1}{2} {mω}^{2} y^{2}}{\frac{1}{2} {mω}^{2} a^{2}} = \frac{y^{2}}{a^{2}}$
So $\frac{2 .5}{E} = \frac{{(\frac{a}{2})}^{2}}{a^{2}}$ $\Rightarrow E = 10 J$

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