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Chapter 2 - Second Order Linear Differential Equations

The king is dead, long live the king. The second order has begun\ldots oh wait, that's not what this is about.

If ever you felt the need to work with simple mass, damper, spring machines or electronic circuits, this chapter is for you. Here we explore linear differential equations containing second derivatives, but nothing higher.

$$y''+a_1y'+a_2y=F(x)$$

Section 2.3 - Second Order Homogeneous Constant Coefficient Linear DE

$$y''+a_1y'+a_2y=0$$

Mass, damper, spring, and no driving force; that's what we're talking about. This section explores the first step in analyzing the spring portion of suspension, as far as I'm concerned.

The Method of Undetermined Coefficients

$$y''+a_1y'+a_2y=F(x)\ \ni\ F(x)\in\{Ae^{ax},A\cos bx+B\sin bx, Ax^k\}$$

Now we get a driving force, but we only look at a couple cases where the function is similar to the solutions we get from the constant coefficient equations.