This problem is an example of critically damped harmonic motion. A mass m = 2 kg is attached to both a spring with spring constant k = 162 N/m and a dash-pot with damping constant c = 36 N -s/m The ball is started in motion with initial position zo = 9 m and initial velocity vo = -83 m/s. Determine the position function (t) in meters. x(t) = Graph the function z(t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t) = Cocos (wotao). Determine Co, wo and co. Co= Wo= 0 = (assume 0 ao < 2) Finally, graph both function (t) and u(t) in the same window to illustrate the effect of damping.