Q119 / 200 · NEET 2024 (Re-NEET) · Physics

A particle executing simple harmonic motion with amplitude $A$ has the same potential and kinetic energies at the displacement

A
$2 \sqrt{A}$
B
$\frac{A}{2}$
Correct answer
C
$\frac{A}{\sqrt{2}}$
D
$A \sqrt{2}$

Solution

Potential energy $=\frac{1}{2} k x^2$ Kinetic energy $=\frac{1}{2} k A^2-\frac{1}{2} k x^2$ According to given condition $\frac{1}{2} k x^2=\frac{1}{2} k A^2-\frac{1}{2} k x^2$ $k 2 x^2=k A^2$ $x^2=\frac{A^2}{2}$ $x=\frac{A}{\sqrt{2}}$

Hence, the correct answer is option: 'C'.

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