Thank you for the reply. A is find the spring force (i used hooke's law) and B is find the damper and any other forces acting. I only got 3 forces: the weight of the mass, the spring and the damper. When using Newton's second law I can some up with a differential equation similar to the one stated in D but I have a -mg and I don't know where the my^.. came from. I've looked at many examples and they always give a negative mg if the unit vector is pointing upwards. Y is a resultant force of an earthquake but I thought this this would be sinusoidal with a sin or cos function. The -mg and the inserted my are the two parts that completely baffle me. C is also mildly confusing. I get the displacement vector for the mass from the origin to be: d+y-x, I understand that differentiating this with respect to time twice would get the acceleration but what would this denote?.... is this where the my and negative mg come from?