Ok, I was given: Solve the following using superposition:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\ddot{x}+2\dot{x}+4x=\delta(t)[/tex]

bounded by [tex]\dot{x}=0, x(0)=0[/tex]

I solved the Homo eqn and got the following:

[tex]x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t))[/tex]

I also know that :

[tex]\ddot{x}+2\dot{x}+4x=u(t)[/tex]

equals

[tex]x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t))+\frac{1}{4}[/tex] from a previous problem.

So, I said:

[tex]x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t))+\frac{\delta (t)}{4}[/tex]

Is this correct thus far (the superposition part at least I'm pretty sure the diff eq portion is correct).

How do I deal with the delta function? Any help would be much appreciated!!!

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# Homework Help: Diff Eq and the Dirac Delta(impulse) function.

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