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Consider the system shown below. Assume that the system is subject to an impulse velocity input = 38(t)Nm, where 8(t) is the impulse function, and initial conditions 0₁ (0) = 1rad, 0(0) = Orad, 0₁ (0) = -2rad/s, and ₂(0) = Orad/s. The angular displacement of the massless connector is given by 0(t). An unknown moment (not pictured) drives the massless connector at a known angular velocity, de. Determine the time domain solution for ₁ (t). Use system parameters I = 1 kg ·m², k = 3 N.m/rad, and 3 = 2N-m-s/rad. dt If you let 9₁ represent the state variable associated with the left disk and q2 represent the state variable associated with the right most disk and q3 associated with the spring and the input is the angular velocity of the middle connector. You should get the following state-space representation: 91 8-88-0-- 92 93 92 = -1 0₁ + de/dt В ÖÖ´Ö™ 02 Figure 2: System for problem 6

Consider the system shown below. Assume that the system is subject to an impulse velocity input = 38(t)Nm, where 8(t) is the impulse function, and initial conditions 0₁ (0) = 1rad, 0(0) = Orad, 0₁ (0) = -2rad/s, and ₂(0) = Orad/s. The angular displacement of the massless connector is given by 0(t). An unknown moment (not pictured) drives the massless connector at a known angular velocity, de. Determine the time domain solution for ₁ (t). Use system parameters I = 1 kg ·m², k = 3 N.m/rad, and 3 = 2N-m-s/rad. dt If you let 9₁ represent the state variable associated with the left disk and q2 represent the state variable associated with the right most disk and q3 associated with the spring and the input is the angular velocity of the middle connector. You should get the following state-space representation: 91 8-88-0-- 92 93 92 = -1 0₁ + de/dt В ÖÖ´Ö™ 02 Figure 2: System for problem 6

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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Consider the system shown below. Assume that the system is subject to an impulse velocity input = 38(t)N m, where 8(t) is the impulse function, and initial conditions 0₁ (0) = 1rad, 0(0) = Orad, 0₁ (0) = −2rad/s, and ₂(0) = Orad/s. The angular displacement of the massless connector is given by 0(t). An unknown moment (not pictured) drives the massless connector at a known angular velocity, de. Determine the time domain solution for ₁(t). Use system parameters I = 1 kg ·m², k = 3 N·m/rad, and 3 = 2N-m.s/rad. dt If you let 9₁ represent the state variable associated with the left disk and q2 represent the state variable associated with the right most disk and q3 associated with the spring and the input is the angular velocity of the middle connector. You should get the following state-space representation: 91 8-88-04- 92 + [₁]. 93 = 01 de/dt K В Ò÷Ö÷´Ø® 02 Figure 2: System for problem 6
Transcribed Image Text:Consider the system shown below. Assume that the system is subject to an impulse velocity input = 38(t)N m, where 8(t) is the impulse function, and initial conditions 0₁ (0) = 1rad, 0(0) = Orad, 0₁ (0) = −2rad/s, and ₂(0) = Orad/s. The angular displacement of the massless connector is given by 0(t). An unknown moment (not pictured) drives the massless connector at a known angular velocity, de. Determine the time domain solution for ₁(t). Use system parameters I = 1 kg ·m², k = 3 N·m/rad, and 3 = 2N-m.s/rad. dt If you let 9₁ represent the state variable associated with the left disk and q2 represent the state variable associated with the right most disk and q3 associated with the spring and the input is the angular velocity of the middle connector. You should get the following state-space representation: 91 8-88-04- 92 + [₁]. 93 = 01 de/dt K В Ò÷Ö÷´Ø® 02 Figure 2: System for problem 6
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