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(B) The total energy $E$ of a particle in simple harmonic motion is given by $E = \frac{1}{2} m \omega^2 a^2$.The kinetic energy $K$ at a displacement

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$y = a/2$

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(B) The total energy $E$ of a particle in simple harmonic motion is given by $E = \frac{1}{2} m \omega^2 a^2$.The kinetic energy $K$ at a displacement $y$ is given by $K = \frac{1}{2} m \omega^2 (a^2 - y^2)$.Taking the ratio of kinetic energy to total energy:$\frac{K}{E} = \frac{\frac{1}{2} m \omega^2 (a^2 - y^2)}{\frac{1}{2} m \omega^2 a^2} = \frac{a^2 - y^2}{a^2} = 1 - \frac{y^2}{a^2}$.Given that $K = 3E/4$,we have:$\frac{3E/4}{E} = 1 - \frac{y^2}{a^2}$.$\frac{3}{4} = 1 - \frac{y^2}{a^2}$.$\frac{y^2}{a^2} = 1 - \frac{3}{4} = \frac{1}{4}$.Taking the square root of both sides,we get $y = a/2$.

$A$ particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy is $E$. At one instant,its kinetic energy is $3E/4$. Its displacement at that instant is:

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