Friction also creates acceleration proportional to the negative of the velocity (see Section 2.10, Exercise 39). A simple case obeys the equation

Write this as a pair of coupled differential equations for x and v.
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:

=--2x-20. dt2 dex 2 2