Aforce of 400 newtons stretches a spring 2 meters. a mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. after finding the equation of motion, calculate x(t = pi/12).

If we start taking into account the free body diagram, we then start damping motion of a body by means of this equation:
m * d^2 x/dt^2 + c* dx/dt + k* x = 0 

free undamped motion is when (c =0) 
therefore 
50* d^2 x/dt^2 + 200* x = 0 
w = omega = sqrt(k/m) = sqrt(200/50) = 2 

Then  

A*cos(w*t) + B*sin(w*t) = x 

find A and B using intial conditions and you will get the rest that you need. Hope this helps