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A particle is vibrating simple harmonically with an amplitude 'a' . Tlte displacement of the particle when its energy is half kinetic and half potential is

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$\frac{a}{2}$

$\frac{a}{\sqrt{2}}$

$\frac{a}{4}$

zero

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Detailed Solution

Kinetic energy = Potential energy

$\frac{1}{2} {mω}^{2} (a^{2} - y^{2}) = \frac{1}{2} {mω}^{2} y^{2}$

$a^{2} - y^{2} = y^{2}$

$2 y^{2} = a^{2} \Rightarrow y = \pm \frac{a}{\sqrt{2}}$

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