Ch 6.4 - 33E
Chapter 6, Problem 33E(choose chapter or problem)
Use the change of variables \(s=\frac{2}{\alpha} \sqrt{\frac{k}{m}} e^{-\alpha t / 2}\) to show that the differential equation of the aging spring \(m x^{\prime \prime}+k e^{-\alpha t} x=0, \alpha>0\), becomes
\(s^{2} \frac{d^{2} x}{d s^{2}}+s \frac{d x}{d s}+s^{2} x=0\)
Text Transcription:
s=frac2alphasqrtfrackme^-alphat/2
mx^prime\prime+ke^-alphatx=0,alpha>0
s^2fracd^2xds^2+sfracdxds+s^2x=0
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