Chapter 17.3, Problem 12E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Consider a spring subject to a frictional or damping force.

(a) In the critically damped case, the motion is given by *x = c*_{1}*e ^{r}*

(b) In the overdamped case, the motion is given by *x =*
*r*_{1} *> r*_{2}*.* Determine a condition on the relative magnitudes of *c*_{1}and *c*_{2} under which the graph of *x* crosses the *t*-axis at a positive value of *t*.

To determine

**To show:** The graph of
*t*-axis whenever

Explanation

**Given data:**

The motion is given as follows,

Consider the motion expression as follows.

If
*t*-axis, then

Substitute

(b)

To determine

A condition on the relative magnitudes of
*t*-axis at a positive value of *t*.

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