A force F ext ( t )= F 0 [ 1?exp(?? t ) ] acts, for time t > 0, on an oscillator

Question

A force Fext(t)= F0[ 1?exp(??t) ] acts, for time t > 0, on an oscillator which is at rest at x=0 at time 0.
The mass is m; the spring constant is k; and the damping force is ?bx?. The parameters satisfy these relations:
b = m q , k = 4 m q2 where q is a constant with units of inverse time.
Find the motion. Determine x(t); and hand in a qualitatively correct graph of x(t).
(B) Determine the final position.

I've done this so far, but I'm not sure how to proceed for the final postion because I feel I need the final time first.

Explanation / Answer

1.At t=0, use x=0 and v=0 -----rest.

2.Final posn-------Limit t tends to infinity on x(t)

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