You posted this in the algebra forum but I'm guessing that actually you are in a class that uses calculus, right? First set up the differential equation for a spring-mass system. From F=ma you have kx = ma, and since a = second derivative of x with respect to time, you have the differential equation:
The general solution to this is , where is amplitude, is rotatonal velocity in radians/second and is the phase angle at t=0. From initial conditions you know A = 10mm and is - do you see why that is? Now solve the initial differential equation for in terms of m and k. From here you can solve the first three questions. The final question will be apparent once you have the expression for . Hope this helps.