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(B) The total energy $E$ of a body executing simple harmonic motion $(SHM)$ is given by $E = \frac{1}{2} m \omega^2 a^2$,where $a$ is the amplitude.At

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$\frac{3 E}{4}$

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(B) The total energy $E$ of a body executing simple harmonic motion $(SHM)$ is given by $E = \frac{1}{2} m \omega^2 a^2$,where $a$ is the amplitude.At any displacement $y$,the potential energy $U$ is given by $U = \frac{1}{2} m \omega^2 y^2$.The kinetic energy $K$ is the difference between total energy and potential energy: $K = E - U$.Substituting the expressions,$K = \frac{1}{2} m \omega^2 a^2 - \frac{1}{2} m \omega^2 y^2 = \frac{1}{2} m \omega^2 (a^2 - y^2)$.Given that the displacement $y = \frac{a}{2}$,we substitute this into the kinetic energy formula:$K = \frac{1}{2} m \omega^2 (a^2 - (\frac{a}{2})^2) = \frac{1}{2} m \omega^2 (a^2 - \frac{a^2}{4}) = \frac{1}{2} m \omega^2 (\frac{3a^2}{4})$.Since $E = \frac{1}{2} m \omega^2 a^2$,we can write $K = \frac{3}{4} (\frac{1}{2} m \omega^2 a^2) = \frac{3E}{4}$.

The total energy of a body executing simple harmonic motion is $E$. When the displacement is half of the amplitude,the kinetic energy is:

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