Question

A mass m is suspended by massless spring by spring constant k the suspension point pulled with upward acceleration a. find the Hamiltonian of the system​

Answer 1

Answer:

Let the initial length of the spring is l. When one mass m is suspended, the string will stretch by amount x from B to C and when mass M is suspended, the string will stretch by amount y from C to D.

Thus, the equation of motion of the system, (M+m)g=−k(x+y)....(1)

When M is removed, the equation of motion will be , mg=−kx...(2)

Using (1) and (2), we get Mg=−ky

or y=−Mg/k

Thus the amplitude of the oscillation is y=Mg/k

Hope it helps you dear friends...