The motion of the piston of an automobile engine is approximately simple harmonic. The stroke of an engine (from the highest point to the lowest point) is 0.100 m and the engine runs at 4500 rev/min. The piston has a mass of 0.45 kg. The equation of the motion is x(t) = Acos(wt + φ). Recall 2π rad = 1 rev. If the piston is said to be at the max positive position at t = 0, write the equations of the position, velocity, and acceleration as functions of time. Calculate the acceleration of the piston at the endpoint of its stroke. What force is exerted on the piston at the endpoint of its stroke? What is the speed and kinetic energy of the piston at the midpoint of its stroke? What average power is required to accelerate the piston from rest to the maximum speed?