A block of mass 12.0 kg is connected to a spring on a horizontal frictionless surface. The spring constant is 200 N/m. The block spring system undergoes simple harmonic motion.

At a time t = 0 seconds, the position of the block x = -80.0 cm and its velocity v = 3.65 m/s.

a. Determine the angular frequency and period of the motion.

b. Determine the amplitude

c. Determine the phase angle

d. prepare the expression for the position of the block as a function of time

e. Determine the position at time = 3.00 s

f. Determine the velocity at time = 3.00 s

g. Determine the acceleration at time = 3.00 s

h. Determine the potential energy of the system when the block is at x = 45.0 cm

i. Determine the block's position when its kinetic energy is 80.0J

j. Determine the total mechanical of the system (E) when the block is moving through its equilibrium position (x=0)