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Question

The angular frequency of a spring block system is ω0. This system is suspended from the ceiling of an elevator moving downwards with a constant speed v0. The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming that downwards is a positive direction, choose the wrong statement.

A
The amplitude of the block is v0ω0.
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B
The initial phase of the block is π.
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C
The equation of motion for the block is v0ω0sinω0t.
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D
The maximum speed of the block is v0
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Solution

The correct option is C The initial phase of the block is π.
Block will be at mean position with velocity v0 as the lift stops, and will try to move downwards due to the inertia of motion. and will start executing SHM, with maximum velocity v0. Since natural frequency of the spring is ω0, amplitude of the motion will be v0ω0. Expression for SHM will be v0ω0sinω0t

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