Consider the double mass / triple spring system shown beloun WWWWWWWWWW springs have spring constant k=7 and all masses have mass m=1kg. spring is subject to a damping force of Ffriction = -3X, Using the standard conversion to a first-order system, he would obtain the system Each 0100 -14 -3 7 0 0001 27 0 14-35 All W³³ (+) = W = Aw / where (t) = The eigenvalues of A are approximately. 712 -1.5±4.33; and 713,4 -1.5 ± 2.187 The eigenvector for 21-1.5 +4.331 is approximately eigenvector for 3-1.5 +2.18 is approximately ) Xilt) xỉ (t X2 ( t) X₂ (+)) 0.07 +0.2/ -007-021; 1 _0.21 -0.31 -0.210.31 1 +27 +211 √i - 1.5+4.33%- / (a). Write general solution wit) of system of the differential equation above (b). Find an initial condition that will result in the masses displaying simple oscillations at relatively high frequency I the fart mode) provided the relaity is zero at to. Jutify the your answer. and the (01 Suppose that there is no friction, i.e., Friction -0. Which of the following could be an eigenvalue of the now corresponding matrix A?. √21
Consider the double mass / triple spring system shown beloun WWWWWWWWWW springs have spring constant k=7 and all masses have mass m=1kg. spring is subject to a damping force of Ffriction = -3X, Using the standard conversion to a first-order system, he would obtain the system Each 0100 -14 -3 7 0 0001 27 0 14-35 All W³³ (+) = W = Aw / where (t) = The eigenvalues of A are approximately. 712 -1.5±4.33; and 713,4 -1.5 ± 2.187 The eigenvector for 21-1.5 +4.331 is approximately eigenvector for 3-1.5 +2.18 is approximately ) Xilt) xỉ (t X2 ( t) X₂ (+)) 0.07 +0.2/ -007-021; 1 _0.21 -0.31 -0.210.31 1 +27 +211 √i - 1.5+4.33%- / (a). Write general solution wit) of system of the differential equation above (b). Find an initial condition that will result in the masses displaying simple oscillations at relatively high frequency I the fart mode) provided the relaity is zero at to. Jutify the your answer. and the (01 Suppose that there is no friction, i.e., Friction -0. Which of the following could be an eigenvalue of the now corresponding matrix A?. √21
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
Related questions
Question
![Consider the double mass / triple spring system shown belown
WWWWWWWW
All
springs
have spring constant k=7 and all masses have mass m=1kg.
Each spring is subject to a damping force of Ffriction = -3X, Using the
standard conversion to a first-order system, he would obtain the
system
0100
-14 -3 7 0
0001
0 14-3
W²³³ (+) =
7
W = Aw, where w(t) =
The eigenvalues of A are approximately.
71,2 -1.5±4.33; and 713,4 -1.5 ± 2.18%
The eigenvector for 2₁-1.5 +4.331 is approximately
eigenvector for 73 -1.5 +2.18; is approximately
Xilt)
xỉ (t
X2 (t)
X₂(+))
0.07 +0.21t
-1
-007-0.21₂
0.21 -0.31ż
1
-0.21 -0.31
and the
(a). Write general solution wilt) of system of the differential equation above
(b). Find an initial condition that will result in the masses displaying simple
oscillations at relatively high frequency I the fart mode) provided the relacity
is zero at t-o. Jutify the your answer.
[c]. Suppose that there is no friction, i.e., Friction -o. Which of the following
could be an eigenvalue of the new corresponding matrix A?.
तरा, नश + नये, √, - 1.5+4337.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf58e778-209d-4051-b758-0c57e3f8187c%2F47eff050-fb4d-437e-a557-4f758352cdfd%2Fmac4orp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the double mass / triple spring system shown belown
WWWWWWWW
All
springs
have spring constant k=7 and all masses have mass m=1kg.
Each spring is subject to a damping force of Ffriction = -3X, Using the
standard conversion to a first-order system, he would obtain the
system
0100
-14 -3 7 0
0001
0 14-3
W²³³ (+) =
7
W = Aw, where w(t) =
The eigenvalues of A are approximately.
71,2 -1.5±4.33; and 713,4 -1.5 ± 2.18%
The eigenvector for 2₁-1.5 +4.331 is approximately
eigenvector for 73 -1.5 +2.18; is approximately
Xilt)
xỉ (t
X2 (t)
X₂(+))
0.07 +0.21t
-1
-007-0.21₂
0.21 -0.31ż
1
-0.21 -0.31
and the
(a). Write general solution wilt) of system of the differential equation above
(b). Find an initial condition that will result in the masses displaying simple
oscillations at relatively high frequency I the fart mode) provided the relacity
is zero at t-o. Jutify the your answer.
[c]. Suppose that there is no friction, i.e., Friction -o. Which of the following
could be an eigenvalue of the new corresponding matrix A?.
तरा, नश + नये, √, - 1.5+4337.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 21 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning