Math 306 - Lab 3
Linear Systems with a parameter

This lab is due Tuesday, March 24th, in class.

IMPORTANT: The work you submit should be your own and nobody else's. Any exceptions to this will be dealt with harshly.

The purpose of this lab is to analye the behavior of the linear system

dx/dt = y
dy/dt = -Bx - cy

as c ranges over all real numbers. As usual, B is the last nonzero digit of your UB person number. This system is a model for a damped harmonic oscillator, with spring constant B and damping constant (or coefficient of friction) c. In this lab, however, we will allow the damping to be negative.

The origin is an equilibrium. As c varies, the nature of the equilibrium at the origin changes.

1. First list your person number and the value B.

2. Determine for which values of c (if any) the origin is

3. For each of a)-g) in part 2. with some parameter values, pick a value of c and use Maple to plot a phaseportrait with a few solution curves. So, e.g., if the origin is a sink for -2 < c < 2, pick one of these values of c and plot a phase portrait. If the origin is a saddle for c > 12, again, pick one of these values of c and draw another plot.