The angular frequency of a spring block system is _0. This system… - Vidyadip

MCQ

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 :

A
The amplitude of the block is $\frac{v_0}{\omega _0}$
✓
The initial phase of the block is $\pi .$
C
The equation of motion for the block is $\frac{v_0}{\omega _0} \sin \omega _0\,t.$
D
The maximum speed of the block is $v_0.$

✓

Answer

Correct option: B.

The initial phase of the block is $\pi .$

b
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.

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