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A spring mass system is hanging from the...

A spring mass system is hanging from the celling of an elevator in equilibrium. The elevator suddenly starts accelerating upwards with acceleration a. Find

(a) the frequency and
(b) the amplitude of the resulting SHM.

Text Solution

Verified by Experts

(i) Frequency =`2pisqrt(m//k)`
(Frequency is independent of g in spring)
(ii) Initial extension in spring in equilibrium `=(mg)/(k)`
Extension in spring in equilibrium when lift starts accelerating upwards `=(m(g+a))/(k)`
`therefore` Amplitude `=(m(g+a))/(k)-(mg)/(k)=(ma)/(k)`
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