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The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100 N/m, k₂ = 50 N/m,k3 = 75 N/m, k4 = 100 N/m, ks = 25 N/m, b₁ = 5 Ns/m, b2 = 7 Ns/m and b3 = 1.5 Ns/m. Displacement input is a unit step. displacement input K₁ ww x₁ (t) m1 E x₂(t) K4 W E b₂ x3(t) m3 m2 ground 1. Derive the dynamic system's mathematical model 2. Determine the dynamics system's transfer functions 3. Determine a state space representation of the dynamic system 4. Plot the system's response, X₁ X2 and x3 on the same graph 5. Plot the system's velocity, xi xż and x3 on the same graph 6. Determine the dynamics system's characteristic equation 7. Determine the roots of the characteristic equation K5 w b3 E 8. What can you conclude about the system based on the roots determined earlier 9. With b2 being a design variable, select an appropriate b2 such that the dynamic system has an overall damping factor of = 0.4

The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100 N/m, k₂ = 50 N/m,k3 = 75 N/m, k4 = 100 N/m, ks = 25 N/m, b₁ = 5 Ns/m, b2 = 7 Ns/m and b3 = 1.5 Ns/m. Displacement input is a unit step. displacement input K₁ ww x₁ (t) m1 E x₂(t) K4 W E b₂ x3(t) m3 m2 ground 1. Derive the dynamic system's mathematical model 2. Determine the dynamics system's transfer functions 3. Determine a state space representation of the dynamic system 4. Plot the system's response, X₁ X2 and x3 on the same graph 5. Plot the system's velocity, xi xż and x3 on the same graph 6. Determine the dynamics system's characteristic equation 7. Determine the roots of the characteristic equation K5 w b3 E 8. What can you conclude about the system based on the roots determined earlier 9. With b2 being a design variable, select an appropriate b2 such that the dynamic system has an overall damping factor of = 0.4

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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The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100 N/m, k₂ = 50 N/m, k3 = 75 N/m, k4 = 100 N/m, ks = 25 N/m, b₁ = 5 Ns/m, b2 = 7 Ns/m and b3 = 1.5 Ns/m. Displacement input is a unit step. displacement input k₁ www x₁ (t) m1 K₂ M b₁₁ E k3 x₂(t) K4 W F b₂ X3 (t) m3 m2 ground 1. Derive the dynamic system's mathematical model 2. Determine the dynamics system's transfer functions 3. Determine a state space representation of the dynamic system 4. Plot the system's response, X₁ X2 and x3 on the same graph 5. Plot the system's velocity, xi xż and x3 on the same graph 6. Determine the dynamics system's characteristic equation 7. Determine the roots of the characteristic equation K5 b3 HE 8. What can you conclude about the system based on the roots determined earlier 9. With b2 being a design variable, select an appropriate b2 such that the dynamic system has an overall damping factor of 33 = 0.4
Transcribed Image Text:The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100 N/m, k₂ = 50 N/m, k3 = 75 N/m, k4 = 100 N/m, ks = 25 N/m, b₁ = 5 Ns/m, b2 = 7 Ns/m and b3 = 1.5 Ns/m. Displacement input is a unit step. displacement input k₁ www x₁ (t) m1 K₂ M b₁₁ E k3 x₂(t) K4 W F b₂ X3 (t) m3 m2 ground 1. Derive the dynamic system's mathematical model 2. Determine the dynamics system's transfer functions 3. Determine a state space representation of the dynamic system 4. Plot the system's response, X₁ X2 and x3 on the same graph 5. Plot the system's velocity, xi xż and x3 on the same graph 6. Determine the dynamics system's characteristic equation 7. Determine the roots of the characteristic equation K5 b3 HE 8. What can you conclude about the system based on the roots determined earlier 9. With b2 being a design variable, select an appropriate b2 such that the dynamic system has an overall damping factor of 33 = 0.4
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