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# Unit II: Second Order Constant Coefficient Linear Equations

#### Contents

Unit Introduction

The general solution to second order differential equations with constant coefficients is:

{$$x = x_h + x_{p^\prime}$$}

where {$x_h$} is the solution to the homogeneous equation of the form:

{$$ax^{\prime\prime} + bx^{\prime} + cx = 0$$}

and {$x_p$} is the particular solution to the inhomogeneous equation

{$$ax^{\prime\prime} + bx^{\prime} + cx = f(t)$$}.

{$f(t)$} is called the forcing term or input, and special consideration is given to the cases in which it is sinusoidal, {$f(t) = B \cos \omega t$}.

Sources:

• Periodic response of a second order system. Modeled on the MIT mathlet Amplitude and Phase: Second Order I.

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