Question

A spring mass system is hanging from the ceiling of a lift. It has been like this for quite some time. Suddenly the cables holding the lift are cut. What will be the amplitude of oscillation of the block when observed by a person standing (of mass M) in the lift?

(a) mg/k

(b) (M-m)g/k

(c) The observer will not observe a SHM

(d) 2mg/k

This question was posed to me in an online interview.

I'd like to ask this question from Oscillations in chapter Oscillations of Physics – Class 11

Answer 1

Correct option is (a) mg/k

To elaborate: When the system was stationary, the extension in the spring will be xo such that kxo= mg or x0 = mg/k.

When the cables are cut, the entire system will be in free fall.                                                                                 The observer will add a pseudo force on the block upwards and equal to mg.

Now the spring has an extension of mg/k                                                                                                                    and the restoring force by the spring will be corresponding to this extension,                                                                   so the amplitude of SHM for the observer is mg/k.