Chapter 17.3, Problem 5E

### 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 3, find the mass that would produce critical damping.

To determine

To find: The mass that produce critical damping.

Explanation

Given data:

The spring is stretched beyond its natural length, so x=âˆ’0.5 , restoringâ€‰force=6â€‰N , dampingÂ constant=14 .

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’0.5â€‰m for x and 6â€‰N for restoring force in equation (1),

6â€‰N=âˆ’k(âˆ’0.5â€‰m)k=6â€‰N0

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