Explanation Procedure used: Consider the distance of the mass beyond the equilibrium position x ( t ) . Write the expression for the Newton’s second law of motion. F n e t = m a Write the expression for the net force acting on the mass. F n e t = F 1 + F 2 + F 3 Here, weight of the mass is F 1 , restoring force is F 2 and damping force is F 3 . Considering damping force on the mass proportional to the instantaneous velocity of the mass. Calculation: Damping force of the mass is, F 3 = − β d x d t Restoring force is, F 2 = − K ( s + x ) Here, negative sign indicates force is acting opposite to weight of the mass. Stiffness of the spring is K and initial displacement is s . Weight of the mass is, F 1 = m g Substitute − K ( s + x ) for F 2 , − β d x d t for F 3 and m g for F 1 in the expression for the net force acting on the mass. F n e t = m g + ( − K ( s + x ) ) + ( − β d x d t ) = m g − K x − K s − β d x d t However, at the condition of equilibrium, m g = K s

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 1.3, Problem 20E

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The differential equation for the displacement of the system.

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Chapter 1.3, Problem 19E

Chapter 1.3, Problem 21E

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The differential equation for the displacement of the system.

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