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A mass m=4 kg is attached to both a spring with spring constant k= 577 N/m and a dash-pot with damping constant e= 4N-s/m. The mass is started in motion with initial position za =1 m and initial velocity ty-3 m/s. Determine the position function z(t) in meters. z(t) = e^t-5t)cos(121)+1/6e^(-5t)sin(12t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form z(t) - Cie cos(wit - a1). Determine C, an a and p. (assume 0Sa, < 2m)

A mass m=4 kg is attached to both a spring with spring constant k= 577 N/m and a dash-pot with damping constant e= 4N-s/m. The mass is started in motion with initial position za =1 m and initial velocity ty-3 m/s. Determine the position function z(t) in meters. z(t) = e^t-5t)cos(121)+1/6e^(-5t)sin(12t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form z(t) - Cie cos(wit - a1). Determine C, an a and p. (assume 0Sa, < 2m)

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 = 577 N/m and a dash-pot with damping constant c=4N-5/m. The mass is started in motion with initial position za = 1 m and initial velocity ty - 3 m/s. Determine the position function z(t) in meters. F(t) = e^(-5t)cos(12t)+1/6e^(-5t)sin(121) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can bo written in the form z(t) - Ciecos(wit - a1). Determine C, wi aand p. C = (assume 0Saj < 2n) Graph the function z(t) together with the "amplitude envelope" curves a= -Cie and z= Cie. 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 – an). Determine Co, ab and ao. Co = (assume 0< ao < 2n) Finally, graph both function r(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 = 577 N/m and a dash-pot with damping constant c=4N-5/m. The mass is started in motion with initial position za = 1 m and initial velocity ty - 3 m/s. Determine the position function z(t) in meters. F(t) = e^(-5t)cos(12t)+1/6e^(-5t)sin(121) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can bo written in the form z(t) - Ciecos(wit - a1). Determine C, wi aand p. C = (assume 0Saj < 2n) Graph the function z(t) together with the "amplitude envelope" curves a= -Cie and z= Cie. 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 – an). Determine Co, ab and ao. Co = (assume 0< ao < 2n) Finally, graph both function r(t) and u(t) in the same window to illustrate the effect of damping
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