Chapter 17.3, Problem 6E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# For the spring in Exercise 4, find the damping constant that would produce critical damping.

To determine

To find: The damping constant that produce critical damping.

Explanation

Given data:

The spring is stretched beyond its natural length, so x=âˆ’0.25 , m=2â€‰kg , restoringâ€‰force=13â€‰N .

Formula used:

Write the expression for Hookeâ€™s Law.

restoringâ€‰force=âˆ’kx (1)

Here,

k is spring constant, and

x is difference between the natural length and length of due to force exerts.

Write the condition for critical damping,

c2âˆ’4mk=0 (2)

Here,

c is damping constant,

k is spring constant, and

m is mass.

Substitute âˆ’0.25â€‰m for x and 13â€‰N for restoring force in equation (1),

13â€‰N=âˆ’k(âˆ’0

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