A box B of mass M hangs from an ideal spring of force constant k. A small particle, also of mass M, is stuck to the ceiling of the box and the system is in equilibrium. The particle gets detached from the ceiling and falls to strike the floor of the box. It takes time t for the particle to hit the floor after it gets detached from the ceiling. The particle, on hitting the floor, sticks to it and the system thereafter oscillates with a time period T. Find the height H of the box if it is given that `t=(T)/(6sqrt(2))`. Assume that the floor and ceiling of the box always remian horizontal.

Answer

`H=(Mg)/(2k)(1+(pi^(2))/(9))`