Explanation A mass lying on a flat dry frictionless surface is attached to the free end of a spring whose constant is k as shown below in Figure 1. From Figure 1 , it is observed that the mass moves along a frictionless surface so the mass of the object has no input in terms of the net force on the spring. Consider Hooke’s law, where k is a spring constant and x is the displacement of spring, the only force on the spring when not at equilibrium is given below. F = − k x ...... ( 1 ) From Newton’s second law, the expression of F is given below. F = m a ...... ( 2 ) where F is the net force, m is the mass of the object and a is the acceleration. Compare equation (1) and equation (2). − k x = m a Acceleration is the second derivative of the displacement so substitute d 2 x d t 2 for a in above equation. − k x = m d 2 x d t 2 m d 2 x d t 2 + k x = 0 Therefore, the differential equation for horizontal spring mass system is m d 2 x d t 2 + k x = 0 . A mass is attached to the spring whose constant is k as shown below in Figure 2.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 3, Problem 53CR

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The differential equations for the displacement x(t) of the freely sliding mass and also discuss the difference between the horizontal and the vertical spring mass system.

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Chapter 3, Problem 51CR

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Advanced Engineering Mathematics

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The differential equations for the displacement x ( t ) of the freely sliding mass and also discuss the difference between the horizontal and the vertical spring mass system.

Solution Summary: The author analyzes the differential equations for the displacement of a freely sliding mass and the difference between the horizontal and vertical spring mass systems.

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The differential equations for the displacement x(t) of the freely sliding mass and also discuss the difference between the horizontal and the vertical spring mass system.

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Chapter 3 Solutions