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Exponential Forcing Differential Equation
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[QUOTE="Alettix, post: 5736975, member: 519608"] [h2]Homework Statement [/h2] Solve ## \frac{d^2y}{dt^2} + \omega^2y = 2te^{-t}## and find the amplitude of the resulting oscillation when ##t \rightarrow \infty ## given ##y=dy/dt=0## at ##t=0##. [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] I have found the homogenious solution to be: ##y_h = A\cos\omega t + B\sin\omega t ## where A and B are constants. When looking for the particular integral I tried the obvious choice ##y_p = Cte^{-t}##. However, unless I have done a misstake this yields an equation system: ##(1+\omega^2)Cte^{-t} = 2te^{-t}## ##-2e^{-t}=0## which lacks solution. Any ideas what more I should try? I can see that as ##t\rightarrow \infty## the forcing term will tend to ##0## and hence the final amplitude should be ##\sqrt{A^2+B^2}##, but I would like to find the solution to the equation.. Many Thanks! :) [/QUOTE]
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Exponential Forcing Differential Equation
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