if m1 =1 , m2 =1, c=2, k1 =3, k2 =2 and all initial conditions are zero, how can I solve this by Laplace transform?

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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if m=1 , m2 =1, c=2, k1 =3, k=2 and all initial conditions are zero, how can I solve this by Laplace transform? 

4) Consider the following mass spring damper system:
k2
m2
u(t)
Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying
the Newton's second law:
+25, = mÿ (i.e. RHS is positive)
Then, equations are written as:
m,ÿ, = k2(V2 – Y1) – kıyı – cy, (1)
mąy, = u(t)
- k2(V2 – 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) = 1 and G2(s) = 26)
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).
%3D
Transcribed Image Text:4) Consider the following mass spring damper system: k2 m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: +25, = mÿ (i.e. RHS is positive) Then, equations are written as: m,ÿ, = k2(V2 – Y1) – kıyı – cy, (1) mąy, = u(t) - k2(V2 – 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) = 1 and G2(s) = 26) 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). %3D
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