Question

Two particles $P$ and $Q$ describe S.H.M. of same amplitude a, same frequency $f$ along the same straight line. The maximum distance between the two particles is $a\sqrt{2}$ The initial phase difference between the particle is

• A. zero
• B. $\pi /2$
• C. $\pi /6$
• D. $\pi /3$

Answer 1

Answer: (B)

$\left|x_1-x\right|=2a\sin \left(\omega +\frac{{\varphi }_1+{\varphi }_2}{2}\right)\cos \left(\frac{{\varphi }_1-{\varphi }_2}{2}\right)$
To maximize
$\left|x_1-x_2\right|:\sin \left(\omega t+\frac{{\varphi }_1+{\varphi }_2}{2}\right)=1$
$\Rightarrow a\sqrt{2}=2a\times 1\times \cos \left(\frac{{\varphi }_1-{\varphi }_2}{2}\right)$
$\Rightarrow \frac{1}{\sqrt{2}}=\cos \left(\frac{{\varphi }_1-{\varphi }_2}{2}\right)$
$\Rightarrow \frac{\pi }{4}=\frac{{\varphi }_1-{\varphi }_2}{2}$
$\Rightarrow {\varphi }_1-{\varphi }_2=\frac{\pi }{2}$