Derive the equations of motion of the following systems in matrix
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Derive the equations of motion of the following systems in matrix
![Equation of motion is in the form of
(0)
(m) (ä) + (el(k) + (k] {x}
Where (x), (m), (c) and (k) are as follows for each system.
m1
X1
1.
[m] =
m2
(x) -
X2
m3
- K1
- k2
k + k2
- k2
Ik)
- k1
(c) -
kz + k3
--1
X1
2.
m2
X2
[m) =
(x) =
X3
4
- K.
- k1
- k2
- k3
k1 + k2
Ik] =
(e) = (0)
K3
+ k
- * 2
3.
[m] =
0.
m 2
(x) -
X2
*3
- C2
C1 + C2
- c2
c2 + C3
- C3
(e) =
- C3
+ CA
03
- K5
- k3
- *2
k2 + ks
- K2
- k5
+
k2 + k3
(k] =
- k3
k3 + k4 + k5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0e13caa-4085-490a-9953-b9a2fd8f2da1%2F38d819a1-411d-44f0-8bae-c33700f3f30c%2F2qqh2d3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Equation of motion is in the form of
(0)
(m) (ä) + (el(k) + (k] {x}
Where (x), (m), (c) and (k) are as follows for each system.
m1
X1
1.
[m] =
m2
(x) -
X2
m3
- K1
- k2
k + k2
- k2
Ik)
- k1
(c) -
kz + k3
--1
X1
2.
m2
X2
[m) =
(x) =
X3
4
- K.
- k1
- k2
- k3
k1 + k2
Ik] =
(e) = (0)
K3
+ k
- * 2
3.
[m] =
0.
m 2
(x) -
X2
*3
- C2
C1 + C2
- c2
c2 + C3
- C3
(e) =
- C3
+ CA
03
- K5
- k3
- *2
k2 + ks
- K2
- k5
+
k2 + k3
(k] =
- k3
k3 + k4 + k5
Transcribed Image Text:Derive the equations of motion of the following systems in matrix form.
1,
Om2
K3
Qm3
m4
k
k.
2
k5
ww
3.
k1
k2
k3
K4
m
m.
"1
C1
C2
C3
C4
2.
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