Write the velocity v in terms of the derivative of the position x, and the acceleration in terms of the derivative of the velocity v. Use the spring equation to write the derivative of the velocity in terms of the position x. Write the spring equation as a pair of equations for position and velocity.
The spring equation or simple harmonic oscillator

studied in Subsection 2.10.3 describes how acceleration (the second derivative of the position x) is equal to the negative of the position. The spring constant k has been set to 1 for simplicity. This one equation for the second derivative can be written as a system of two autonomous differential equations.

Transcribed Image Text:

dex 2 2