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4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: F, = mỹ (i. e. RHS is positive) Then, equations are written as: m,ỹi = k2(V2 – Y1) – k,yı – cy, (1) m2y2 = u(t) - k2(y2 – Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and ki = 10 N/m, k2 = 20 N/m. Then, answer the following questions. a) Find the transfer functions G,(s) = 1O and G2(s) = 4O U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ÿ; (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y,(s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if,

4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: F, = mỹ (i. e. RHS is positive) Then, equations are written as: m,ỹi = k2(V2 – Y1) – k,yı – cy, (1) m2y2 = u(t) - k2(y2 – Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and ki = 10 N/m, k2 = 20 N/m. Then, answer the following questions. a) Find the transfer functions G,(s) = 1O and G2(s) = 4O U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ÿ; (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y,(s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if,

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Inverse Laplace

4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: F, = mỹ (i. e. RHS is positive) Then, equations are written as: m,ỹi = k2(V2 – Y1) – k,yı – cy, (1) m2y2 = u(t) - k2(y2 – Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and ki = 10 N/m, k2 = 20 N/m. Then, answer the following questions. a) Find the transfer functions G,(s) = 1O and G2(s) = 4O U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ÿ; (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y,(s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if,
Transcribed Image Text:4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: F, = mỹ (i. e. RHS is positive) Then, equations are written as: m,ỹi = k2(V2 – Y1) – k,yı – cy, (1) m2y2 = u(t) - k2(y2 – Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and ki = 10 N/m, k2 = 20 N/m. Then, answer the following questions. a) Find the transfer functions G,(s) = 1O and G2(s) = 4O U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ÿ; (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y,(s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if,
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