A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{4}\]
Correct Answer: C
Solution :
\[{{x}_{1}}=A\sin \omega \,t\] \[{{x}_{2}}={{x}_{0}}+A\sin (\omega t+\phi )-A\sin \omega t\] Separation \[{{x}_{0}}+A\sin (\omega t+\phi )-A\sin \omega t\] \[={{x}_{0}}+2A\sin i\left( \frac{\phi }{2} \right)\cos \omega t\] Maximum separation \[={{x}_{0}}+2A\sin \frac{\phi }{2}={{x}_{0}}+A\] \[\Rightarrow \,\,\phi =\frac{\pi }{3}\]
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