Question

The equation of motion of a simple harmonic motion is

• A. $\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}x$
• B. $\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}t$
• C. $\frac{d^{2}x}{d{t}^2}=-\omega x$
• D. $\frac{d^{2}x}{d{t}^2}=-\omega t$

Answer 1

The correct option is A $\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}x$

The simple equation of motion of simple harmonic motion is given by

$x=Asin\omega t$. . . . . . . . .(1)

Differentiate the above equation with respect to the time,

$\frac{dx}{dt}=A\omega cos\omega t$

Again differentiate with respect to time,

$\frac{d^{2}x}{d{t}^2}=-A{\omega }^{2}sin\omega t$

$\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}x$

The correct option is A.