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 = 8 N /m and a dash-pot with damping constant c = 8 N - s/m . The ball is started in motion with initial position 3:0 = 3 m and initial velocity v0 = 11 m/s. Determine the position function a:(t) in meters. :c(t) = \\\\ Graph the function :c(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 (wot an). Determine Cg, we and a0. 00: (1)0: // /, a0 = / (assume 0 3 am