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Math Help - Damped Spring problem

  1. #1
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    Damped Spring problem

    The position y(t) of a damped spring satisfies the differential equation y''+2y'+5y=0. Determine y(t) when the initial position is y(0) and the initial velocity is y'(0)=1?
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  2. #2
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    Re: Damped Spring problem

    This type of differential equation is solved by substituting y=e^{rt} to get the characteristic equation r^2+2r+5=0. This equation has two roots that are complex conjugates, a+bi and a-bi, so the general solution is e^{at}(C_1\cos{bt}+C_2\sin{bt}). You can use the initial conditions to find C_1 and C_2.

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