How Does a Damped Oscillator Behave with Different Initial Conditions?

[coffeem]

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.


MY ATTEMPT AT ANSWER

a) Can do fine. No probems with this.

b) Setting t = 0 gives x = A

So I am 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.

 

[alphysicist]

Hi cofeem,

You found that A=Ao by setting t=0 in the x(t) expression and knowing that it must equal Ao.

The other initial condition deals with the velocity. Since you know x(t), how do you find v(t)? What do you get? Then you can do the same thing with v(t) to find B that you did with x(t) to find A.