Question

The phase difference between the displacement and acceleration of a particle in a simple harmonic motion is

• A. $\frac{\pi }{2}\text{rad}$
• B. Zero
• C. $\pi \text{rad}$
• D. $\frac{3\pi }{2}\text{rad}$

Answer 1

The correct option is C $\pi \text{rad}$


For simple harmonic motion of a system, displacement is given by

$x=A\sin \omega t$


So, acceleration of the system will be

$a=\frac{d^{2}x}{d{t}^2}=-A{\omega }^2\sin \omega t=A{\omega }^2\sin (\omega t+\pi )$

From both expression, phase difference between the displacement and acceleration of a particle in a simple harmonic motion is $\pi$.

Hence, option $\left(c\right)$ is correct.