Solution Found!
(a) Show that the solution of the initial-value problem
Chapter 5, Problem 39E(choose chapter or problem)
(a) Show that the solution of the initial-value problem
\(\frac{d^{2} x}{d t^{2}}+\omega^{2} x=F_{0} \cos \gamma t, \quad x(0)=0, \quad x^{\prime}(0)=0\)
is \(x(t)=\frac{F_{0}}{\omega^{2}-\gamma^{2}}(\cos \gamma t-\cos \omega t)\).
(b) Evaluate \(\lim _{\gamma \rightarrow \omega} \frac{F_{0}}{\omega^{2}-\gamma^{2}}(\cos \gamma t-\cos \omega t)\).
Text Transcription:
fracd^2xdt^2+omega^2x=F_0cos\gammat,x(0)=0,x^prime(0)=0
x(t)=F_0omega^2-gamma^2(\cosgammat-cosomegat)
lim_gammaomegafracF_0omega^2-gamma^2cos\gammat-cosomegat)
Questions & Answers
QUESTION:
(a) Show that the solution of the initial-value problem
\(\frac{d^{2} x}{d t^{2}}+\omega^{2} x=F_{0} \cos \gamma t, \quad x(0)=0, \quad x^{\prime}(0)=0\)
is \(x(t)=\frac{F_{0}}{\omega^{2}-\gamma^{2}}(\cos \gamma t-\cos \omega t)\).
(b) Evaluate \(\lim _{\gamma \rightarrow \omega} \frac{F_{0}}{\omega^{2}-\gamma^{2}}(\cos \gamma t-\cos \omega t)\).
Text Transcription:
fracd^2xdt^2+omega^2x=F_0cos\gammat,x(0)=0,x^prime(0)=0
x(t)=F_0omega^2-gamma^2(\cosgammat-cosomegat)
lim_gammaomegafracF_0omega^2-gamma^2cos\gammat-cosomegat)
ANSWER:Step 1 of 9
In this problem, we need to solve the given initial-value problem
