Calc III Lab: Introduction
In this lab we will study both linear and nonlinear oscillators, and
discover a few differences between the two classes of oscillators.
A linear (harmonic) oscillator may be modelled by
the differential equation
dx/dt = v
dv/dt = -damping v -x + tau.
Here damping>0 is a parameter called the coefficient of damping. It reflects
the amount of dissipation in the oscillator. If damping=0,
then there is no friction; if damping is large, then
trajectories are quickly pulled into a sink (meaning that the motion stops).
The parameter tau reflects a constant external force that
affects the system.
Objectives of the lab
The objectives of this lab are
- to understand the dynamics of forced, damped oscillators.
- to compare the dynamics of linear oscillators with the dynamics
of nonlinear oscillators.
Getting Started with DsTool
You will need to launch DsTool for this lab.
DsTool has an on-line help
facility to help you in doing the exercises below.
Outline of the Lab
Robert E. Thurman <thurman@geom.umn.edu>
Last modified: Mon Nov 20 13:21:13 1995