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Applets
Here are several applets demonstrating concepts discussed in MAT 303 (will open in new windows):
- Mechanical Vibrations:
- Free damped vibrations
- This is the graph of the solution of the equation x''+bx'+kx=0. You may vary parameters b and k and the initial values
x(0) and x'(0) (just click on the b or k slides in the lower left corner or the x(0)-x'(0) plane above them to change the
values). Clicking on the Roots
button will show the roots of the corresponding characteristic equation.
- Non-free damped
vibrations
- This is the graph of the solution of the equation x''+bx'+kx=cos(ωt). Here you may also change the values of b, k,
x(0) and x'(0) as well as the external frequency ω. The blue graph on the right corresponds to the solution of the
associated homogeneous equation, xc, the green graph to the particular solution xp. The yellow graph is
the solution x=xc+xp.
- Systems of equations:
- Phase Portraits
- To work with this applet, turn off the "Companion Matrix" feature (click on the blue square to the left of the words
"Companion Matrix").
- In the lower right corner, you have the slides for parameters a,b,c,d. Above is the phase portrait for the
system
x'=ax+by
y'=cx+dy
Changing values of these parameters changes the phase portrait.
All applets are courtesy of the d'Arbeloff Interactive Math Project at MIT.
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