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Get Full Access to A First Course In Differential Equations With Modeling Applications - 10 Edition - Chapter 5.r - Problem 13e
Get Full Access to A First Course In Differential Equations With Modeling Applications - 10 Edition - Chapter 5.r - Problem 13e

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# A force of 2 pounds stretches a spring 1 foot. With one

ISBN: 9781111827052 44

## Solution for problem 13E Chapter 5.R

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 13E

A force of 2 pounds stretches a spring 1 foot. With one end held fixed, a mass weighing 8 pounds is attached to the other end. The system lies on a table that imparts a frictional force numerically equal to times the instantaneous velocity. Initially, the mass is displaced 4 inches above the equilibrium position and released from rest. Find the equation of motion if the motion takes place along a horizontal straight line that is taken as the x-axis.

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NEWTON’S FIRST LAW ● the most profound change in understanding the universe up to his time ● developed in the 1660s when the plague was sweeping thru Europe - again ● not published for almost 20 years ● perhaps a true law of nature ● objects at rest stay at rest ● objects in motion stay in motion, unless acted on by an outside force ● the first was common sense ● the 2nd was revolutionary ● the natural state of anything… what it will do if you leave it alone… is uniform motion ○ constant speed in a straight line ● moving uniformly feels like being at rest ● you can’t feel motion, only changes in motion ● there is no such thing as centrifugal force = term comes from misunderstanding the first law

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A force of 2 pounds stretches a spring 1 foot. With one