A block of mass m is suspended from the ceiling of a stationary standig elevator through a spring of spring constant k. Suddenly, the cable breaks and the elevator starts falling freely. Show that the bklock now executes a simple harmonic motion of amplitude `mg/k` in the elevator

Explanation

When the elevator is statioN/Ary the spring is stretched to support the block. If the extension is x, the tension is kx which should balance the weight of the block

Thus `x=mg/k`. As the cable breaks the elevator starts falling with acceleratio g. e shall work in the frame of reference fo the elevator. THen we have to use a pseudo force mg upward on teh blck. This force will balance the weight. Thus, the block is subjected to net force kx by the spring hasrmonic with its measn position corresponding to the unstretched spring. Initially the spring is stretched by `x=mg/k`, where the velocity of the block (with respect to the elevator) is zero. Thus, the amplitude of the resulting simple harmonic motion is `mg/k`.