A spring mass system is hanging from the ceiling of an elevator in equilibrium. Elongation of spring is l. The elevator suddenly starts accelerating downwards with acceleration g/3, find: (a) the frequency and (b) the amplitude of the resulting SHM.

Question

G1 Physics · Accepted Answer

Initially kl=mg, so k/m=g/l and f=(1/2π)√(g/l). When the elevator accelerates downward at g/3, effective gravity is 2g/3, giving new equilibrium extension 2l/3. The mass was initially at extension l, so displacement from the new equilibrium is l/3; this is the amplitude. Thus all four options are correct.