: A mass m = 4 kg is attached to both a spring with spring constant k = 325 N/m and a dash-pot with damping constant c = 4 N. s/m. The mass is started in motion with initial position zo = 3 m and initial velocity vo = 6 m/s. Determine the position function (t) in meters. x(t) = Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form (t) = C₁e pt cos(wit - α₁). Determine C₁, W₁.0₁and p. C₁ = W₁ = α₁ = (assume 0 ≤ α₁ <2) P = Graph the function z(t) together with the "amplitude envelope" curves a = -Cie Pt and a C₁e=pt I = 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 ag. Co = Wo= α0 (assume 0 < a < 2π) Finally, graph both function (t) and u(t) in the same window to illustrate the effect of damping.