Question

A spring mass system is hanging from the ceiling of an elevator in equilibrium. The elevator suddenly starts accelerating upwards with accelerating a, consider all the options in the reference frame of elevator.

• A. the frequency of oscillation is $\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
• B. the amplitude of the resulting SHM is $\frac{ma}{k}$
• C. amplitude of resulting SHM is $\frac{m(g+a)}{k}$
• D. maximum speed of block during oscillation is $\left(\sqrt{\frac{m}{k}}\right)a$

Answer 1

The correct option is B the amplitude of the resulting SHM is $\frac{ma}{k}$

Frequency =$2\pi \left(m/k\right)$ frequecy is independent of $g$ in spring

Extension in spring in equilibrium

initial $=\frac{mg}{k}$

Extension in spring in equilibrium in accelerating lift $m(g+a)$

Amplitude $=\frac{m\left(g+a\right)}{k}-\frac{mg}{k}=\frac{ma}{k}$