For the following system of coupled differential equations, write the matrix representation of a system of blocks and springs as an equivalent system of first-order equations. d?x,2.dt2dx1+5-5dtdx2+ 12x1 – 2x2 = 0dtd²x23dt21dx1dx2- 2x1 + 2x2 = 0dt5.+5.dt1a. A=-6- 2.512.50.66 -0.661.66 -1.661b. A =-6- 2.5-12.50.66 -0.66 1.66 -1.66|11с.A =-61- 2.52.50.66 -0.66 -1.66 1.6611d. A =- 6-1- 2.52.5- 0.66 -0.66 1.66 -1.661.

Given, 2d2x1dt2+5dx1dt-5dx2dt+12x1-2x2=03d2x2dt2-5dx1dt+5dx2dt-2x1+2x2=0 Let u1=x1v1=x1˙=u1˙

Answered: d²x, 2 dx, dt dx2 + 12x1 – 2x2 = 0 dt²…

d²x, 2 dx, dt dx2 + 12x1 – 2x2 = 0 dt² dt d²xz 3- dt2 1 dx1 5. 5. dt Txp° dt dx2 - 2x, + 2x2 = 0 1 a. A= -6 1 - 2.5 2.5 | 0.66 -0.66 1.66 -1.66| 1 1

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

For the following system of coupled differential equations, write the matrix representation of a system of blocks and springs as an equivalent system of first-order equations.

d?x,
2.
dt2
dx1
+5-
5
dt
dx2
+ 12x1 – 2x2 = 0
dt
d²x2
3
dt2
1
dx1
dx2
- 2x1 + 2x2 = 0
dt
5.
+5.
dt
1
a. A=
-6
- 2.5
1
2.5
0.66 -0.66
1.66 -1.66
1
b. A =
-6
- 2.5
-1
2.5
0.66 -0.66 1.66 -1.66|
1
1
с.
A =
-6
1
- 2.5
2.5
0.66 -0.66 -1.66 1.66
1
1
d. A =
- 6
-1
- 2.5
2.5
- 0.66 -0.66 1.66 -1.66
1.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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