1. Total energy in SHM

For a block executing simple harmonic motion, the total mechanical energy is constant:

$E = \frac{1}{2}kA^2$

The maximum potential energy occurs at the extreme position $x=A$, and it equals the total energy.

Given:

$U_{\max} = 25\,\text{J}$

So,

$E = 25\,\text{J}$

2. Potential energy at displacement $x = A/2$

In SHM, potential energy at displacement $x$ is

$U = \frac{1}{2}kx^2$

At $x = A/2$,

$U = \frac{1}{2}k\left(\frac{A}{2}\right)^2 = \frac{1}{2}k\cdot \frac{A^2}{4} = \frac{1}{4}\left(\frac{1}{2}kA^2\right)$

But

$\frac{1}{2}kA^2 = 25$

Hence,

$U = \frac{25}{4} = 6.25\,\text{J}$

3. Kinetic energy at $x = A/2$

Since total energy is conserved,

$K = E - U$

So,

$K = 25 - 6.25 = 18.75\,\text{J}$

4. Match with options

$18.75\,\text{J}$ corresponds to Option C.

5. Comparison with stored answer

Stored correct answer: C

My derived answer: C

They agree.