Numerical Methods For Engineers, 7 Ed
Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 27, Problem 25P

Derive the set of differential equations for a three mass–four spring system (Fig. P27.25) that describes their time motion. Write the three differential equations in matrix form,

[ Acceleration vector ] + [ k / m  matrix ] [ displacement vector  x ] = 0

Note each equation has been divided by the mass. Solve for the eigenvalues and natural frequencies for the following values of mass and spring constants: k 1 = k 4 = 15  N/m,  k 2 = k 3 = 35  N/m, and  m 1 = m 2 = m 3 = 1 .5kg .

Chapter 27, Problem 25P, 27.25	Derive the set of differential equations for a three mass–four spring system (Fig. P27.25)

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Numerical Methods For Engineers, 7 Ed

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