Question

Two particles are in SHM with the same amplitude and frequency along the same line and about the same point. If the maximum separation between them is $\sqrt{3}$ times their amplitude, then the phase difference between them is :

• A. ${47}^o$
• B. ${133}^o$
• C. ${137}^o$
• D. ${43}^o$

Answer 1

The correct option is C ${137}^o$

Maximum separation occurs when one of the particles is at an extreme position.

Let us assume -ve extreme.
The other is at $(\sqrt{3}-1)A$ from mean.
$(\sqrt{3}-1)A=A\sin \varphi$
$\varphi ={\sin }^{-1}(\sqrt{3}-1)$$={47}^0$
The other is at $-{90}^0$.
So, separation is ${137}^0$