A) \[\phi =\frac{\pi }{2}\]
B) \[\phi ={{\cos }^{-1}}\left( \frac{7}{9} \right)\]
C) \[\phi ={{\cos }^{-1}}\left( \frac{3}{7} \right)\]
D) \[\phi =\pi \]
Correct Answer: C
Solution :
Let the equation of SHM be \[{{x}_{1}}=A\,\sin (\omega t)\] \[{{x}_{2}}=A\sin (\omega t+\phi )\] According to contrition, \[\frac{A}{3}=A\sin (\omega t)-\frac{A}{3}=A\sin (\omega t+\phi )\] By solving above equation, \[\phi =\pi \] or \[\cos \phi =\frac{7}{9}\] Also, \[{{v}_{1}}=A\omega \cos (\omega t),\] \[{{v}_{2}}=A\omega \cos (\omega t+\phi )\] For velocities in same direction, \[\phi ={{\cos }^{-1}}\left( \frac{7}{9} \right)\]You need to login to perform this action.
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