First slide

Simple hormonic motion

Question

A particle is executing SHM. At a point $x = \frac{A}{3}$ , kinetic energy of the particle is K, where A is the amplitude. At a point x = $\frac{2 A}{3}$ , kinetic energy of the particle will be:

Moderate

A

2 K
B

$K \sqrt{2}$
C

$\frac{5}{8} K$
D

$\frac{5}{3} K$

Solution

$v = ω \sqrt{(A^{2} - x^{2})} \Rightarrow v \propto \sqrt{(A^{2} - x^{2})}$
At x = $\frac{A}{3}$
$\sqrt{(A^{2} - x^{2})} = \sqrt{(A^{2} - \frac{4 A^{2}}{9})} = A \sqrt{\frac{8}{9}}$
At x = $\frac{2 A}{3}$
$\sqrt{(A^{2} - x^{2})} = \sqrt{(A^{2} - \frac{4 A^{2}}{9})} = A \sqrt{\frac{5}{9}}$
$K^{'} = \frac{5}{9} \times \frac{9}{8} K = \frac{5}{8} K$

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