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)

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