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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- Nov 28th 2012, 06:39 AMchizmin10Damped 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?

- Nov 28th 2012, 08:41 AMhollywoodRe: Damped Spring problem
This type of differential equation is solved by substituting to get the characteristic equation . This equation has two roots that are complex conjugates, and , so the general solution is . You can use the initial conditions to find and .

- Hollywood