# Damped Oscillator Question?

The equation for motion for a damped oscillator is:

x(double dot) + 2x(dot) + 2 = 0

a) Show that x(t)= (A + Bt)e^-t

Where A and B are constants, satisfies the equation for motion given above.

b) At time t = 0, the oscillator is released at distance Ao from equilibrium and with a speed Uo towards the equilibrium position. Find A and B for these initial conditions.

c) Sketch the t-dpendence of x for the case in which Ao = 20m and Uo =25m/s and the case in which Ao = 20m and Uo =10m/s.

a) Can do fine. No probems with this.

b) Setting t = 0 gives x = A

So im assuming as x = Ao then A - Ao.

However I do not know how to get further than this.

c) Dont know how to do this. Am assuming that once you have the relationships between Ao, Uo, A and B then you will be able to just plug the numbers in and graph the function.

Thanks for any help.