MATH 322 - MATLAB GUIs
Vibrating String
© GUI developed by
Joceline Lega, Spring
2007.
Description
This MATLAB GUI illustrates the use of Fourier
series to simulate the dynamics of a vibrating
string. The string is clamped at its end points and
its deflection from the horizontal, u,
evolves according to the wave equation,
utt - uxx =
0.
- The initial condition is decomposed into a
Fourier series by finding its half-range sine
expansion;
- The corresponding coefficients are evolved in
time. Fifty Fourier modes are included in the
simulation. The evolution of the amplitudes of
modes zero through ten is shown in a bar
graph.
- The resulting Fourier series, giving the
shape of the string, is calculated and plotted at
each time step.
The GUI also illustrates the fact that the
simulated solution may be written as the sum of two
traveling waves, one propagating to the left, and
the other propagating to the right.
How to use the GUI
- To start, place the cursor on the string,
left-click and drag to define an initial
deflection, then release the left mouse button.
The initial velocity is automatically set to zero
and the string starts vibrating.
- Select the Left TW and/or Right
TW check boxes to see the corresponding left-
and/or right-going waves.
- Select the Superposition check box to
see the sum of the left- and right- traveling
waves that describe the deflection of the
string.
- The Reset button reinitializes the
GUI.
Download
Download (right click on each link below)
the following files into a directory. Set the
MATLAB path to that directory and type
Vibrating_String at the MATLAB
prompt.
Type help
Vibrating_String at the MATLAB prompt if you
need to be reminded of how to use the GUI.
