Using the mass–spring analogy, predict the behavior as of
Chapter 4, Problem 31E(choose chapter or problem)
Using the mass-spring analogy, predict the behavior as \(t \rightarrow+\infty\) of the solution to the given initial value problem. Then confirm your prediction by actually solving the problem.
(a) \(y^{\prime \prime}+16 y=0 ; y(0)=2, y^{\prime}(0)=0\)
(b) \(y^{\prime \prime}+100 y^{\prime}+y=0 ; y(0)=1, y^{\prime}(0)=0\)
(c) \(y^{\prime \prime}-6 y^{\prime}+8 y=0 ; y(0)=1, y^{\prime}(0)=0\)
(d) \(y^{\prime \prime}+2 y^{\prime}-3 y=0 ; y(0)=-2, y^{\prime}(0)=0\)
(e) \(y^{\prime \prime}-y^{\prime}-6 y=0 ; y(0)=1, y^{\prime}(0)=1\)
Equation Transcription:
Text Transcription:
t right arrow + infinity
y''+16y=0; y(0)=2, y'(0)=0
y''+100y'+y=0; y(0)=1, y'(0)=0
y''-6y'+8y=0; y(0)=1, y'(0)=0
y''+2y'-3y=0; y(0)=-2, y'(0)=0
y''-y'-6y=0; y(0)=1, y'(0)=1
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