Section 3.7 Free Mechanical Vibratic Problem 4 (1 point) This problem is an example of critically damped harmonic motion. A mass m 2 7 kg is attached to both a spring with spring constant k = 112 N/m and a dash-pot with damping constant c : 56 N - s/m. The ball is started in motion with initial position 3:0 : 6 m and initial velocity '00 : 29 m/s. Determine the position function x(t) in meters. a:(t) = Graph the function 32(75). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so 6 = 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 a0). Determine Co, we and a0. 00 = we : a0 = (assume 0 3 (10