Answer to Question #186990 in Quantum Mechanics for Nishu

Question

A cylinder of mass ( q.m) is connected to an ideal spring with k spring constant. It is also connected to a hanging body of mass( m ) with a rope that goes over a pulley. The mass of the smaller cylinder is negligible. Initially the system is stationary such a way that the spring is undeformed and the hangig body is supported. What will be the angular frequency of the central mass of the cylinder after the support is removed?

What will be the amplitude A of the oscillation of the central mass of the cylinder? 

Answer 1

Tension of the string, $T=mg$

Right after the support is removed,

Force experienced by spring,

$T-kx-qmg=0$

$x=\dfrac{mg-qmg}{k}$

Amplitude of oscillation, $A=\dfrac{mg-qmg}{k}$

Frequency of oscillation $=\sqrt{\dfrac{mg-qmg}{k}}$