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I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly explained. Could anyone explain whether there is an equation to describe the amplitude and if so, whether you could explain to me how you can obtain this formula?

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If you mean the amplitude at resonance then you can looked into "the damped driven harmonic oscillator." There are loads of pages on this thing. It's basically required knowledge for physics students. –  santa claus Jun 16 '13 at 9:19

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