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This problem is an example of critically damped harmonic motion. A mass m = 6 kg is attached to both a spring with spring constant k = 294 N/m and a dash-pot with damping constant c = 84 N-s/m. The ball is started in motion with initial position = 7 m and initial velocity vo = -54 m/s. Determine the position function (t) in meters. r(t) = Graph the function z(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(wotao). Determine Co. wo and co. Co= Wo= ag= (assume 0 < a < 2π) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping.

This problem is an example of critically damped harmonic motion. A mass m = 6 kg is attached to both a spring with spring constant k = 294 N/m and a dash-pot with damping constant c = 84 N-s/m. The ball is started in motion with initial position = 7 m and initial velocity vo = -54 m/s. Determine the position function (t) in meters. r(t) = Graph the function z(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(wotao). Determine Co. wo and co. Co= Wo= ag= (assume 0 < a < 2π) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This problem is an example of critically damped harmonic motion. A mass m = 6 kg is attached to both a spring with spring constant k = 294 N/m and a dash-pot with damping constant c = 84 N. s/m. The ball is started in motion with initial position = 7 m and initial velocity vo = -54 m/s. Determine the position function z(t) in meters. x(t) = Graph the function (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 - ao). Determine Co, wo and an. 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.
Transcribed Image Text:This problem is an example of critically damped harmonic motion. A mass m = 6 kg is attached to both a spring with spring constant k = 294 N/m and a dash-pot with damping constant c = 84 N. s/m. The ball is started in motion with initial position = 7 m and initial velocity vo = -54 m/s. Determine the position function z(t) in meters. x(t) = Graph the function (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 - ao). Determine Co, wo and an. 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.
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