Question

The phase difference between displacement and acceleration of a particle performing SHM is?

Answer 1

Step 1: Displacement:

Displacement can be written as $x=A\sin wt....\left(1\right)$

Here, $A$is amplitude and $w$ is angular velocity.

Step 2: Acceleration:

Accleration can be written as

$$\begin{gathered} a=\frac{d^{2}x}{d{t}^2} \\ =\frac{d^2}{d{t}^2}\left(A\sin wt\right) \\ =Aw\frac{d}{dt}\left(\cos wt\right) \\ =A{w}^2\sin \left(\mathrm{\pi }+\mathrm{wt}\right).....\left(2\right) \end{gathered}$$

From equations (1) and (2), the phase difference is π radian.

Hence, the phase difference between displacement and acceleration of the particle is π radian.