Question

A spring mass system hanging from the ceiling of an elevator is at rest. The elevator starts accelerating upwards with acceleration 'a'. 'm' is the mass of block and 'k' is the spring constant of spring. Then choose the correct alternative(s).

• A. Amplitude of oscillation is $\frac{ma}{k}$
• B. Amplitude of oscillation is $\frac{mg}{k}$
• C. Time period of oscillation is $2\pi \sqrt{\frac{m}{k}}$
• D. Time period of oscillation is $2\pi \sqrt{\frac{2m}{k}}$

Answer 1

Answer: (A), (C)

The correct options are
A Amplitude of oscillation is $\frac{ma}{k}$
C Time period of oscillation is $2\pi \sqrt{\frac{m}{k}}$

When the lift starts to accelerate upwards, an extra force (pseudo - force) acts on the mass in the downward direction as we see from accelerating frame of reference. Hence $kA=ma$ or $A=ma/k$ where $A$ is the amplitude or maximum displacement for the spring . The pseudo force is the restoring force and hence the time period of oscillation does not change . $T=2\pi \sqrt{\frac{m}{k}}$