1550078481-Ordinary_Differential_Equations__Roberts_

Answers to S elected Exercises

Chapter 9 APPLICATIONS OF LINEAR SYSTEMS

WITH CONSTANT COEFFICIENTS

Exercises 9.1 Coupled Spring-Mass Systems

1. a.

(

• .467992) ( .000000)
  .000000. - .999527

u = c 1 {cos 2.13578x. 131401 - sm 2.13578x .OOOOOO }

.000000 .280644

559

. .000000 -. 999527
(

• .467992) ( .000000)

• c 2 { sm 2.13578x. 131401 +cos 2.13578x .OOOOOO }
  .000000 .280644

(

.732913) .000000. (.000000) .485301

+ c 3 {cos .662153x 1. 30515 - sm .662 153 x .OOOOOO }

.000000 .864212

+ c4{sin .662153x ( 1 i~~~~~) +cos .662153x (~~ml)}

.000000 .864212

1. b. u = c1[(cos,8x)v 1 - (sin,8x)v2] + c2[(sin,8x)v 1 + (cos,8x)v 2]

+ c3[(cos1x)v 3 - (sin1x)v4] + c4[(sin1x)v 3 + (cos1x)v4]

where ,8 = 1.93185, ')' = .5 17638 and

(

-. 517362 )

.000000

Vi = .189368 '

.000000

(

.000000)

• .999466

V^2 = .000000 '

.365830

(

1.11 595 )

0.00000

v 3 = 1.52442 ' and

0.00000

(

.000000)

.577659

V^4 = .000000

.789096