STANDARD Physics Simple Harmonic Motion MCQ Question

In the equation of simple harmonic motion $\frac{d^2x}{dt^2} + cx = 0$, the term $c$ represents the angular frequency squared, where $\omega^2 = c$. The time period $T$ of the motion is given by the formula $T = \frac{2\pi}{\omega}$, leading to $T = \frac{2\pi}{\sqrt{c}}$. Therefore, if we let $a = c$, the time period can be expressed as $T = \frac{2\pi}{\sqrt{a}}$, confirming option C as the correct choice. Options A, B, and D do not correctly relate the time period to the angular frequency, making them incorrect.