Is my forced spring-mass system correctly modeled with these equations?

[Shackleford]

After the spring-mass is in equilibrium, a force is applied then released at t₀ and the spring-mass system is set into motion. For a certain period of time the spring-mass will move around the x₀ equilibrium position until the restoring from the spring has balanced the gravitational force.

Are my two equations correct? I guess I'm having trouble accounting for the gravitational force and the forcing term in the DE. Otherwise, it would be a simple homogeneous equation with x = A cos(w₀t).

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-21193429.jpg?t=1285115763

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-21193118.jpg?t=1285115676

 

[Shackleford]

Anyone? Eh?