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second order differential equations & Laplace

Hi all, this is my first post so please bear with me - anyadvice/support would be warmly welcomed. I have been doing some work on asimple RLC electronic circuit whose transfer function follows the standardsecond order transfer function.

The forcing function (input) is a periodic square wavefunction and I am trying to write an equation for the output - time based.

Please find 2 documents attached in which I have tried todevelop equations for the output using 2 different methods. The first one is usingcomplementary function and particular integrals (which I do not like). Thesecond one uses Laplace transforms. I have found a time based equation but wheni input times i do not think i am getting the correct output values. Cansomeone please have a look -

particularly the Laplace pdf.

Many thanks, derek

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Re: second order differential equations & Laplace

Attachment 26883Please forgive me if I havent included enough detail before now but hopefully the attached document will help. It is my attempt to solve exactly the same problem using complementary function and particularly integral. The circuit values are c = 22uF, L = 100uH, Ro=10 ohms. The input forcing function is a periodic square wave with zero offset and does not go negative with amplitude = 23.5v and frequency = 43Khz, T=23.25us, ton=6.43us, toff=16.8us and duty cycle D=0.28.

Kind Regards, derick007