A mass m = 4 kg is attached to both a spring with spring constant k = constant c = 4 N s/m. The mass is started in motion with initial position o 3 m and initial velocity = 5 m/s. Determine the position function z(t) in meters. r(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form r(t) = Ciecos (wit - a). Determine C₁, w₁,ajand p. C₁ W₁ == aj = (e^(-1/2t))[((-5/6) sin(12t))+(3cos (12t))] Co Graph the function z(t) together with the "amplitude envelope" curves z=-C₁e- and z = C₁e. 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-ao). Determine Co. wo and a. والا (assume 0 ≤ a <2m)