2. Consider the setup shown in the figure below used to model passive vibration isolation (where we try to protect the machine from the vibrations coming from the ground). When the distances z = 0 and r 0, the system is in equilibrium. 2.a Derive the equation of motion and write in into state space form by using the state variables w = z - r and v = ż , the input u =r , and the output y =v. Use the standard notation (@n, 5). 2.b Considering an, = 1 [rad/s] and 5= 0.6 calculate the eigenvalues and eigenvectors of the matrix A and calculate the matrix exponential e^. 2.c Using the results in part (b) derive the free response when considering the initial conditions w(0) = w, , v(0) =0.

2. Consider the setup shown in the figure below used to model passive vibration isolation (where we try to protect the machine from the vibrations coming from the ground). When the distances z = 0 and r 0, the system is in equilibrium. 2.a Derive the equation of motion and write in into state space form by using the state variables w = z - r and v = ż , the input u =r , and the output y =v. Use the standard notation (@n, 5). 2.b Considering an, = 1 [rad/s] and 5= 0.6 calculate the eigenvalues and eigenvectors of the matrix A and calculate the matrix exponential e^. 2.c Using the results in part (b) derive the free response when considering the initial conditions w(0) = w, , v(0) =0.

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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