For part b) i), I think the omega squared term is the force due to friction, the term on the right hand side of the equation is the driving force and b/m x' is the damping force? It's been a while since we did this and I can't really remember.
I've uploaded my answer to part b) ii) as it was easier than rewriting on here, have I done it correctly or have I done it completely wrong?
Thanks for the help!
Sorry for the pictures being the wrong way, it won't let me rotate them!