Question

A spring of spring constant $K$ is fixed to the ceiling of a lift. The other end of the spring is attached to a block of mass $m$. The mass is in equilibrium. Now the lift accelerates downwards with an acceleration $2\, g$ :

• A. The block will not perform SHM and it will stick to the ceiling.
• B. The block will perform SHM with time period $2 \pi \sqrt{m / K}$.
• C. The amplitude of the block will be 2 mg/K if it perform SHM.
• D. The min. potential energy of the spring during the motion of the block will be 0 .

Answer 1

Answer: (B), (C), (D)

Due to the Pseudo force on block (considered external) its mean popsition will shift to a distance $m g / K$ above natural length of spring as net force now is $mg$ in upward direction so total distance of block from new mean position is $2\, mg / K$ which will be the amplitude of oscillations hence option $(C)$ is correct. During oscillations spring will pass through the natural length hence option $(D)$ is correct. As block is oscillating under spring force and other constant forces which do not affect the $SHM$ frequency hence option (B) is correct