A mass m = 4 kg is attached to both a spring with spring constant k = 101 N/m and a dash-pot with damping constant c=4N-

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A Mass M 4 Kg Is Attached To Both A Spring With Spring Constant K 101 N M And A Dash Pot With Damping Constant C 4n 1 (28.05 KiB) Viewed 37 times

A mass m = 4 kg is attached to both a spring with spring constant k = 101 N/m and a dash-pot with damping constant c=4N-s/m The mass is started in motion with initial position zo 5 m and initial velocity to = 9 m/s. Determine the position function z(t) in meters. -1/2(e^(-1/2))*(5cos(5t)+(1.3)(sin(5t))) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form r(t) = Cie "cos(wit-a₁). Determine C₁. Waand p. C₁= Wy == a₁ = (assume 0 ≤ a, <2x) p= Graph the function () together with the "amplitude envelope* curves -Cie and C₁e Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (soc=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(watan). Determine Co, wo and oro. Co= Wo (assume 0 a <2m). Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping.