1550078481-Ordinary_Differential_Equations__Roberts_

560

3. a.


4. b.

u'=

Ordinary Differential Equations

-'---(k1 --'---+ k2)u1 - d1u2 --+ --k2u3

m1 m1 m1

U4=^1 ---k2Ul ---k2U3 --d2U4

m2 m2 m2

0 1 0 0

k1 + k2 d1 k2 0

m1 m1 m1

0 0 0 1

k2

0

k2 d2

m2 m2 m2

u

where a= -.75, j3 = 1.31083, a= -.164102, b = -1.33590 and

c.000000 571024 ) - .993552 .0841723

Vi = .445842 '

( 326715 )

V^2 = - .255092 '

c 512927 )

v^3 = -.656944 ' and

.0000 00 .775742 .167806

c (^422975) .565052 )
V^4 = -.541737
.723705

5. a. 0 1 0 0

k1 + k2 d1 kz

0

m1 m1 m1

u'= u

0 0 0 1

k2

0

k2 + k 3 d2

m2 m2 m2