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About LinkBacksThe 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?
This type of differential equation is solved by substitutingto 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
.
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