A block of mass m rests on a flat, frictionless surface and is attached to a spring with spring constant k. The block is set into simple harmonic motion at time t = 0 s from a displacement zo from equilibrium and with a velocity v. For this problem you may find handy: cos² 0 = +cos 20 and sin² 0 = 1/cos 20. COS a) What is the initial energy of the system? What is the angular frequency w? b) In the form r(t) = A cos(wt-o), determine the amplitude A and the phase o from the initial conditions. Write down the equation for the position r(t) in terms of To, Vo, m, and k. c) What is the potential energy stored in the spring U(t), in terms of To, V₁, m, and k? d) Now write down the velocity v(t). e) What is the kinetic energy K(t)? Verify that the sum of the kinetic and potential energy at all times is a constant and matches the initial energy.