Underdamped Harmonic oscillator with applied force

[nbram87]

Homework Statement

An underdamped harmonic oscillator with mass m, spring constant k, and damping resistance c is subject to an applied force F0cosωt.
(a) [analytical] If, at t = 0, x = x0 and v = v0, what is x(t)?

Homework Equations

Ωinitial = √(k/m)

The Attempt at a Solution

Fnet = -kx - cv + F0cos(Ωt) = ma
x(t) = xh(t) (homogeneous) + xi(t) (inhomogeneous) so we will only be left with the inhomogeneous part
x(t) = Acos(Ωt - ∅)

A = (F0/m) / ((√(Ωinitial^2 - Ω^2)^2 + 4gamma*Ω^2))

∅ = tan-1((2*gamma*Ω)/(Ωinitial^2 - Ω^2))

I have all that but I am confused where x = x0 amd v = v0 come into play and how to plug it all into a x(t) equation

 

[Spinnor]

The amplitude should depend on time? Does yours?

See,

http://demonstrations.wolfram.com/DrivenDampedOscillator/

This demo starts with nonzero velocity though.