Solution Found!
Ch 4.1 - 7E
Chapter 4, Problem 7E(choose chapter or problem)
Given that \(x(t)=c_{1} \cos \omega t+c_{2} \sin \omega t\) is the general solution of \(x^{\prime \prime}+\omega^{2} x=0\) on the interval \((-\infty, \quad)\), show that a solution satisfying the initial conditions \(x(0)=x_{0}, x^{\prime}(0)=x_{1}\)is given by
\(x(t)=x_{0} \cos \omega t+\frac{x_{1}}{\omega} \sin \omega t .\)
Text Transcription:
x(t) c1 cos vt c2 sin omegat
x^prime prime + omega^2 x =0
-infty, quad
x(0) = x0, x^prime(0) = x1
x(t)=x_{0} \cos \omega t+\frac{x_{1}}{\omega} \sin \omega t
Questions & Answers
QUESTION:
Given that \(x(t)=c_{1} \cos \omega t+c_{2} \sin \omega t\) is the general solution of \(x^{\prime \prime}+\omega^{2} x=0\) on the interval \((-\infty, \quad)\), show that a solution satisfying the initial conditions \(x(0)=x_{0}, x^{\prime}(0)=x_{1}\)is given by
\(x(t)=x_{0} \cos \omega t+\frac{x_{1}}{\omega} \sin \omega t .\)
Text Transcription:
x(t) c1 cos vt c2 sin omegat
x^prime prime + omega^2 x =0
-infty, quad
x(0) = x0, x^prime(0) = x1
x(t)=x_{0} \cos \omega t+\frac{x_{1}}{\omega} \sin \omega t
ANSWER:Step 1 of 4
In this question, we have to show that the given solution satisfies x(0)= , x’(0) =
.