JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Elasticity & SHM

In simple harmonic motion the total mechanical energy stays constant and equals the maximum potential energy, which is reached at the extreme position where the whole energy is potential; hence the total energy is $E=25$ J. At a displacement $x$ the potential energy is $U=\frac{1}{2}k{x}^2$, so at $x=A/2$ it is $U=\frac{1}{2}k{\left(\frac{A}{2}\right)}^2=\frac{1}{4}\cdot \frac{1}{2}k{A}^2=\frac{E}{4}=\frac{25}{4}=6.25$ J. The kinetic energy is the remainder of the total, $K=E-U=25-6.25=18.75$ J.