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(B) The total energy $E$ of a particle in simple harmonic motion is the sum of its kinetic energy $K$ and potential energy $U$.Given that the kinetic

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

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(B) The total energy $E$ of a particle in simple harmonic motion is the sum of its kinetic energy $K$ and potential energy $U$.Given that the kinetic energy is equal to the potential energy,$K = U$.Since the total energy $E = K + U$,we have $E = 2U$ or $E = 2K$.The potential energy at displacement $y$ is given by $U = \frac{1}{2} m \omega^2 y^2$.The total energy is given by $E = \frac{1}{2} m \omega^2 a^2$.Setting $U = \frac{1}{2} E$,we get:$\frac{1}{2} m \omega^2 y^2 = \frac{1}{2} (\frac{1}{2} m \omega^2 a^2)$$y^2 = \frac{a^2}{2}$$y = \frac{a}{\sqrt{2}}$

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

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