Question

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 that downwards is a positive direction, choose the wrong statement.

• A. The amplitude of the block is $\frac{v_0}{{\omega }_0}$.
• B. 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 1

Answer: (B)

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

Block will be at mean position with velocity $v_0$ as the lift stops, and will try to move downwards due to the inertia of motion. and will start executing SHM, with maximum velocity $v_0$. Since natural frequency of the spring is ${\omega }_0$, amplitude of the motion will be $\frac{v_0}{{\omega }_0}$. Expression for SHM will be $\frac{v_0}{{\omega }_0}\sin {\omega }_{0}t$