Program Explanation Given information: The matrix differential equation for the given system is shown below. x ″ = [ − c 1 c 1 0 c 2 − 2 c 2 c 2 0 c 3 c 3 ] x Here coefficient c i is defined as, c i = k m i The value of mass m 1 and mass m 2 for the given system is written below. m 1 = 750 slugs m 2 = 750 slugs m 3 = 500 slugs The value of spring constant is written as, k = 3000 lb / ft The initial conditions for the system are written as, x 1 ( 0 ) = 0 , x 2 ( 0 ) = 0 , x 3 ( 0 ) = 0 x ′ 1 ( 0 ) = v 0 , x ′ 2 ( 0 ) = 0 , x 3 ( 0 ) = − v 0 Explanation: The matrix differential equation for the given system is written as, x ″ = [ − c 1 c 1 0 c 2 − 2 c 2 c 2 0 c 3 − c 3 ] x The matrix A for the system is written below. A = [ − c 1 c 1 0 c 2 − 2 c 2 c 2 0 c 3 − c 3 ] A = [ − k m 1 k m 1 0 k m 2 − 2 k m 2 k m 2 0 k m 3 − k m 3 ] Substitute the corresponding values from the given information and write as, A = [ − 4 4 0 6 − 12 6 0 4 − 4 ] Use calculator or matrix program to find the eigenvalues and corresponding eigenvectors for the matrix A and obtain the result as, λ 1 = 0 ⇒ v 1 = [ 1 1 1 ] T λ 2 = − 4 ⇒ v 2 = [ 1 0 − 1 ] T λ 3 = − 16 ⇒ v 3 = [ 1 − 3 1 ] T Therefore, the solution vector is written as, x ( t ) = ( a 1 + b 1 t ) v 1 + ( a 2 cos − λ 2 t + b 2 sin − λ 2 t ) v 2 + ( a 3 cos − λ 3 t + b 2 sin − λ 3 t ) v 3 x ( t ) = ( a 1 + b 1 t ) [ 1 1 1 ] + ( a 2 cos 2 t + b 2 sin 2 t ) [ 1 0 − 1 ] + ( a 3 cos 4 t + b

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 5.4, Problem 20P

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Program Description: Purpose of the problem is to show that railway cars separated after π/2 seconds and proceed in their respective ways with constant velocities, also obtain the values of these constant velocities x′1(t) , x′2(t) , and x′3(t) of three cars.

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Chapter 5.4, Problem 19P

Chapter 5.4, Problem 21P

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Chapter 5 Solutions

EBK DIFFERENTIAL EQUATIONS

Ch. 5.1 - Let A=[2347] and B=[3451]. Find (a) 2A+3B; (b)...Ch. 5.1 - Prob. 2P Ch. 5.1 - Find AB and BA given A=[203415] and B=[137032].Ch. 5.1 - Prob. 4P Ch. 5.1 - Prob. 5P Ch. 5.1 - Prob. 6P Ch. 5.1 - Prob. 7P Ch. 5.1 - Prob. 8P Ch. 5.1 - Prob. 9P Ch. 5.1 - Prob. 10P

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Program Description: Purpose of the problem is to show that railway cars separated after π / 2 seconds and proceed in their respective ways with constant velocities, also obtain the values of these constant velocities x ′ 1 ( t ) , x ′ 2 ( t ) , and x ′ 3 ( t ) of three cars.

Solution Summary: The author explains that the problem is to show that railway cars separated after pi /2 seconds and proceed in their respective ways with constant velocities.

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Program Description: Purpose of the problem is to show that railway cars separated after π/2 seconds and proceed in their respective ways with constant velocities, also obtain the values of these constant velocities x′1(t) , x′2(t) , and x′3(t) of three cars.

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Chapter 5 Solutions