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Calculus / Fundamentals of Differential Equations 8 / Chapter 4.8 / Problem 2E

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

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Using the paradigm (13), what are the inertia, damping,

Chapter 4, Problem 2E

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QUESTION:

Using the paradigm (13), what are the inertia, damping, and stiffness for the equation \(y^{\prime \prime}-6 y^{2}=0\)? If \(y>0\), what is the sign of the "stiffness constant"? Does your answer help explain the runaway behavior of the solutions \(y(t)=1 /(c-t)^{2}\)?

Equation Transcription:

$y''-6{y}^{2}=0$

$y>0$

$y(t)=1/(c-t{)}^{2}$

Text Transcription:

y''-6y^2=0

y>0

y(t)=1/(c-t)^2

Questions & Answers

QUESTION:

Using the paradigm (13), what are the inertia, damping, and stiffness for the equation \(y^{\prime \prime}-6 y^{2}=0\)? If \(y>0\), what is the sign of the "stiffness constant"? Does your answer help explain the runaway behavior of the solutions \(y(t)=1 /(c-t)^{2}\)?

Equation Transcription:

$y''-6{y}^{2}=0$

$y>0$

$y(t)=1/(c-t{)}^{2}$

Text Transcription:

y''-6y^2=0

y>0

y(t)=1/(c-t)^2

ANSWER:

SOLUTION
Step 1

We have equation

${F}_{ext}=\ my''+by'+ky$

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