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The angular frequency of a spring block system is $\omega _0.$ This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0.$ The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement :
The amplitude of the block is $\frac{v_0}{\omega _0}$
The initial phase of the block is $\pi .$
The equation of motion for the block is $\frac{v_0}{\omega _0} \sin \omega _0\,t.$
The maximum speed of the block is $v_0.$
Solution
since $V_{0}$ is the maximum speed of the ball in its equilibrium position. $\therefore V_{0}=\omega_{0} A$
$A=\frac{V_{0}}{\omega_{0}}$
So equation of motion becomes $\frac{V_{0}}{\omega_{0}}=A \sin \omega_{0} t$ as there was no initial phase in the $SHM.$
There was no initial phase in the $SHM.$
Hence $B$ is correct.
