(a) Explanation Given: Mass m = 8 kg and spring constant k = 16 . Calculation: The general equation of motion is, m x " + β x ' + k x = 0 ( 1 ) x " + ( 10 ) x ' + ( 16 ) x = 0 x " + 10 x ' + 16 x = 0 Obtain the auxiliary equation and solve as, m 2 + 10 m + 16 = 0 ( m + 2 ) ( m + 8 ) = 0 m 1 = − 2 , m 2 = − 8 So, the solution of differential equation is, x c = c 1 e − 2 t + c 2 e − 8 t . The initial conditions are, x ( 0 ) = 1 and x ′ ( 0 ) = 0 . Use the initial condition x ( 0 ) = 1 and obtain the relation between the constants as, x ( 0 ) = c 1 e 0 + c 2 e 0 1 = c 1 × 1 + c 2 × 1 (b) To determine The equation of motion.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 3.8, Problem 27E

(a)

To determine

The equation of motion.

(b)

To determine

The equation of motion.

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Chapter 3.8, Problem 26E

Chapter 3.8, Problem 28E

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Chapter 3 Solutions

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