Ordinary Differential Equations/Applications of Second Order DEQs

There are several uses for second-order differential equations. In this chapter, I will cover the use of second-order differential equations to describe the motion of a mass at the end of a spring.

The chapter is broken up into three sections:

1. Simple Harmonic Motion
2. Motion with a Damping Force
3. Motion with an Outside Force

Chapter Notation

The formulae in this chapter are written with the following notation in mind. If you've learned a different manner of notation, please take note of the differences. I made every attempt to use a standard set of notation.

Important Terms

Terms that I feel deserve your undivided attention will appear like This. You will see this term referred to often in the text that follows, so it's recommended that you fully understand what it means.

Derivatives with respect to time

If a derivation is taken with respect to time (t), then an equivalent symbol is used and is pronounced x double-dot, x triple-dot, etc.

• Example:${\frac {d^{2}x}{dt^{2}}}\equiv {\ddot {x}}$

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