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.

Answer

A, B

Explanation

(a) Frequency `= (1)/(2pi) sqrt((k)/(m))`
(Frequency is independent of `g` in spring)
(b) Extension in spring in equilibrium
initial `= (mg)/(k)`
Extension in spring in equilibrium in
accelerating lift `=(m(g + a))/(k)`
`:.` Amplitude `= (m(g + a))/(k) - (mg)/(k) = (ma)/(k)`.