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Differential Equations in Control Theory
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Consider the differential equation: $\frac{d^2y}{dt^2} + 2\frac{dy}{dt} + y = 0$. What is the characteristic equation of this differential equation?
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A
$s^2 + 2s + 1 = 0$
💡 Explanation:
The characteristic equation is obtained by replacing $\frac{d}{dt}$ with $s$ in the differential equation. Therefore, the characteristic equation is $s^2 + 2s + 1 = 0$.