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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 = 4 N · s/m. The mass is started in motion with initial position xo = 5 m and initial velocity vo = 3 m/s Determine the position function æ(t) in meters. æ(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form æ(t) = Ce=*cos(wit – a1). Determine C1, wi ,ajand p. C = WI = (assume 0 < aj < 27) Graph the function æ(t) together with the "amplitude envelope" curves a = -Cje-pt and æ = Cie-pt. 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 (wot – ao). Determine Co, wo and ao. Co = wo = (assume 0 < ao < 27 ) Finally, graph both function æ(t) and u(t) in the same window to illustrate the effect of damping.

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 = 4 N · s/m. The mass is started in motion with initial position xo = 5 m and initial velocity vo = 3 m/s Determine the position function æ(t) in meters. æ(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form æ(t) = Ce=*cos(wit – a1). Determine C1, wi ,ajand p. C = WI = (assume 0 < aj < 27) Graph the function æ(t) together with the "amplitude envelope" curves a = -Cje-pt and æ = Cie-pt. 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 (wot – ao). Determine Co, wo and ao. Co = wo = (assume 0 < ao < 27 ) Finally, graph both function æ(t) and u(t) in the same window to illustrate the effect of damping.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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 = 4 N. s/m. The mass is started in motion with initial position xn = 5 m and initial velocity vn = 3 m/s Determine the position function x(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 æ(t) = Cje pt cos(wit – a1). Determine C1, wi ,ajand p. C = (assume 0 < aj < 27) p = Graph the function x(t) together with the "amplitude envelope" curves a = -Cje-pt and r = Ce-pt 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(wat – ao). Determine Co, wo and aæn. Co = wo = (assume 0 < an < 27 ) Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.
Transcribed Image Text: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 = 4 N. s/m. The mass is started in motion with initial position xn = 5 m and initial velocity vn = 3 m/s Determine the position function x(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 æ(t) = Cje pt cos(wit – a1). Determine C1, wi ,ajand p. C = (assume 0 < aj < 27) p = Graph the function x(t) together with the "amplitude envelope" curves a = -Cje-pt and r = Ce-pt 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(wat – ao). Determine Co, wo and aæn. Co = wo = (assume 0 < an < 27 ) Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.
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