Physics - SHM Question with Solution | TestHub

The maximum potential energy of a block executing simple harmonic motion is given by $E=\frac{1}{2}k{A}^2$, which is also equal to the total energy of the system.

The kinetic energy of the block at any displacement $x$ is given by $K=\frac{1}{2}k(A^2-x^2)$.

Substituting $x=\frac{A}{2}$ into the kinetic energy expression:

$K=\frac{1}{2}k\left(A^2-{\left(\frac{A}{2}\right)}^2\right)$

$K=\frac{1}{2}k\left(A^2-\frac{A^2}{4}\right)$

$K=\frac{1}{2}k\left(\frac{3A^2}{4}\right)$

$K=\frac{3}{4}\left(\frac{1}{2}k{A}^2\right)$

Since $E=\frac{1}{2}k{A}^2$, we get:

$K=\frac{3\text{E}}{4}$

Answer: $\frac{3\text{E}}{4}$