First slide

Simple hormonic motion

Question

The total energy of a particle executing SHM is 48 Joule. Then find its potential energy when its displacement is half of the amplitude.

Moderate

A

8 J
B

24 J
C

16 J
D

12 J

Solution

E = Total Energy $= \frac{1}{2} {mω}^{2} A^{2}$
$∴ \frac{1}{2} {mω}^{2} = E / A^{2}$
Now, U = Potential Energy $\frac{1}{2} {mω}^{2} x^{2}$
When $x = \frac{A}{2}, U = (\frac{E}{A^{2}}) \times {(\frac{A}{2})}^{2} = \frac{E}{4} = \frac{48}{4} J = 12 J .$

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