Suppose that the motion of a damped oscillator of mass m2 is

Solution

general solution is x = e^(t)

putting it in diff eqn

2²+2+5 =0

=> = -0.5 ± 1.5i

So final general solution is x = ke^-0.5tcos(1.5t)

as t->

the x will oscillate with amplitude approaching to zero.