Differential equations (swinging door)

[Poetria]

Homework Statement

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There is a swing door with a damper. The characteristic polynomial (I have done it correctly) is:
0.5*r^2+1.5*r+0.625

General solution for x(0)=x_0 and v(0)=v_0 is (I have found it without a problem):

(1.25*x_0+v_0/2)*e^(-0.5*t)+((v_0+0.5*x_0)/(-2))*e^(-2.5*t)

Now the hell begins:
for x(0)=0.25
What can you say about the initial velocity of the door if, once the door is let go, it swings through the closed position and then swings back from the other side? (a numerical value and an appropriate inequality should be given)

The Attempt at a Solution

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Constants c_1 and c_2 given the initial conditions (x_0=0.25).

c_1+c_2=0.25
v_0=(0.25-c_2)*(-0.5)-c_2*(2.5)

The new solution:

(0.25-(v_0+0.125)/(-2))*e^(-0.5*t)+((v_0+0.125)/(-2))*e^(-2.5*t)

Well, now I am at my wits' end. I guess the velocity at the equilibrium position should be less than 0.

 

[Poetria]

Hi, guys, I have solved it at last. No help necessary. Phew.