Newton's Second Law of Motion
as an Ordinary Differential Equation
...using Maple 10
Freefall (as a first-order ODE)
Start "Classic Worksheet Maple 10" and
begin typing-in this Maple program.
(Sorry, you can't cut-and-paste right now.)
I will guide you through this code.
Things to try (and interpret physically).
For your own benefit, you may wish to save your variations with unique filenames.:
- Vary the initial conditions IC and v0.
- Vary m.
- Vary at least two of these variables.
The Oscillator (as a second-order ODE)
This second-order ordinary differential equation
can be handled by writing it as a system of two first-order ordinary differential equations
Using a different filename, type [or cut-and-paste] in this code. (Watch for any stray < bracket symbols.)
Things to try (and interpret physically).
For your own benefit, you may wish to save your variations with unique filenames.:
- Vary the initial conditions IC.
- Vary m.
- Vary k.
- Vary F(t).
- Vary at least two of these variables.
The Damped Oscillator (as a second-order ODE)
Using a different filename, modify the above program to model a damped harmonic oscillator.
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Things to try (and interpret physically).
For your own benefit, you may wish to save your variations with unique filenames.:
- Vary b. (What should happen when b=0?)
- Vary the initial conditions IC.
- Vary m.
- Vary k.
- Vary F(t).
- Vary at least two of these variables.
The Van Der Pol Oscillator (as a nonlinear second-order ODE)
Using a different filename, modify the above program to model a Van Der Pol oscillator.
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Things to try (and interpret physically).
For your own benefit, you may wish to save your variations with unique filenames.:
- Vary mu. (What should happen when mu=0?)
- Vary the initial conditions IC.
- Vary m.
- Vary k.
- Vary F(t).
- Vary at least two of these variables.
- You must try this: (counts as one variation!)
- mu:=5;k:=1;Force(t):=5*cos(2.466*t); then...
mu:=5;k:=1;Force(t):=5*cos(2.466*t); with a slightly nudged initial condition IC.
You will submit [at a time after Spring Break to be determined] as a print-out (or electronically as a "Classic Worksheet")
- Three (3) variations of the damped oscillator,
with a written explanation of your parameters and a brief discussion of your results.
(No two students should have the same set of variations.)
- Three (3) variations of the Van Der Pol oscillator,
with a written explanation of your parameters and a brief discussion of your results.
(No two students should have the same set of variations.
Everyone must try the indicated variation.)
This page will be updated...
