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 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? Correct Answer mg/k

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.
Bissoy MCQ

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