Amass of 0.100 kg is attached to a spring with a spring constant of 40.0 N/m.  The mass is free to move back and forth along a frictionless horizontal surface.  The mass is at rest at the equilibrium position of the spring when it is suddenly hit in such a way to give it a speed of 0.350 m/s in the +x direction at t = 0. 

 (a) (10points) Calculate the period and amplitude of the resulting oscillation.

(b)(10points) Calculate the maximum speed and acceleration of the mass

(c)(20 points)Determine the expressions for the position, velocity, and acceleration as a function of time, taking x(t) = A*cos(ωt + φ).