A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be [2023]

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Solution

Q.
A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be [2023]

1 1 : 1

2 2 : 1

3 1 : 4

4 1 : 3

Ans.
(4)

$x = \frac{A}{2}, P.E. = \frac{1}{2} k x^{2}$

$K.E. = \frac{1}{2} k A^{2} - \frac{1}{2} k x^{2}$

$\frac{P.E.}{K.E.} = \frac{x^{2}}{A^{2} - x^{2}} = \frac{A^{2}}{4 (\frac{3 A^{2}}{4})} = \frac{1}{3}$

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