Rotational inertia

Hi,

I would like to calculate the function of a rotating disc that has 2 spring slowing it down. (look at my pictures to understand)

Let say I turn my disc 90 degrees clockwise and release it, it is going to oscillate a certain moment than stop.



I want to plot that function and to have a sinus function decreasing to 0 after a "x" number of period.

Thanks for your help,
Jean-Philippe