Differentiate the Fourier sine series by term in Problem 18. Show that the result is not the

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Differentiate the Fourier sine series by term in Problem 18. Show that the result is not the derivative of \(f(x)=x\).

Data from Problem 18

An undamped, unforced Duffing Equation, \(\ddot{x}+\omega^{2} x+\epsilon x^{3}=0\), can be solved exactly in terms of elliptic functions. Determine the solution of this equation and determine if there are any restrictions on the parameters.

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