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.m1X11.[m] =m2(x) -X2m3- K1- k2k + k2- k2Ik)- k1(c) -kz + k3--1X12.m2X2[m) =(x) =X34- K.- k1- k2- k3k1 + k2Ik] =(e) = (0)K3+ k- * 23.[m] =0.m 2(x) -X2*3- C2C1 + C2- c2c2 + C3- C3(e) =- C3+ CA03- K5- k3- *2k2 + ks- K2- k5+k2 + k3(k] =- k3k3 + k4 + k5 Derive the equations of motion of the following systems in matrix form.1,Om2K3Qm3m4kk.2k5ww3.k1k2k3K4mm."1C1C2C3C42.

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Math

Advanced Math

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

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