Question

Two particles are executing simple harmonic motion of the same amplitude A and frequency $\omega$ along the x-axis. Their mean position is separated by distance $X_0(X_0>A)$. If the maximum separation between them is ($X_0+A$), the phase difference between their motion is:

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (A)

$\frac{\pi }{3}$

$x1=Asin(\omega t+\varphi 1)$

$x2=Asin(\omega t+\varphi 2)$

$x1-x2=A(2sin(\omega t+\frac{\varphi 1+\varphi 2}{2})sin(\frac{\varphi 1-\varphi 2}{2}))$

$A=2Asin\frac{\varphi 1-\varphi 2}{2}$

$\frac{\varphi 1-\varphi 2}{2}=\frac{\Pi }{6}$

$\varphi 1=\frac{\Pi }{3}$