Question

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

• A. zero
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is B

$\frac{\pi }{2}$

$x_1=asin(\omega t+{\varphi }_1)$

$x_2=asin(\omega t+{\varphi }_2)$

$\Rightarrow |x_1-x_2|=2asin(\omega t+\frac{{\varphi }_1+{\varphi }_2}{2})cos\left(\frac{{\varphi }_1-{\varphi }_2}{2}\right)$

To maximize $|x_1-x_2|:$

$sin(\omega t+\frac{{\varphi }_1+{\varphi }_2}{2})=1$

$\Rightarrow a\sqrt{2}=2a\times 1\times cos\left(\frac{{\varphi }_1-{\varphi }_2}{2}\right)\Rightarrow \frac{1}{\sqrt{2}}=cos\left(\frac{{\varphi }_1-{\varphi }_2}{2}\right)$

$\Rightarrow \frac{\pi }{4}=\frac{{\varphi }_1-{\varphi }_2}{2}\Rightarrow {\varphi }_1-{\varphi }_2=\frac{\pi }{2}$