A particle executes SHM of amplitude . The distance from the mean position when its kinetic energy becomes equal to its potential energy is _______ [2023]

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Solution

Q.
A particle executes SHM of amplitude $A$ . The distance from the mean position when its kinetic energy becomes equal to its potential energy is _______ [2023]

1 $\sqrt{2} A$

2 $2 A$

3 $\frac{1}{\sqrt{2}} A$

4 $\frac{1}{2} A$

Ans.
(3)

$K.E. = P.E.$

$\frac{1}{2} M ω^{2} (A^{2} - x^{2}) = \frac{1}{2} M ω^{2} x^{2}$

$A^{2} - x^{2} = x^{2} \Rightarrow A^{2} = 2 \times 2$

$\Rightarrow x = \pm \frac{A}{\sqrt{2}}$

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