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If you get a "LaTex markup" error on this page, please reload the page to see the equations that use the Latex markup. |
If you have never used MATLAB before, we recommend watching some of these videos from The MathWorks , in particular the Getting Started video. . You can go through the videos either before or after completing this tutorial.
Spring-Mass Harmonic Oscillator in MATLAB
Created using MATLAB R2013a
Problem Specification
Consider a spring-mass system shown in the figure below.
Applying F = ma in the x-direction, we get the following differential equation for the location x(t) of the center of the mass:
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{include: ANSYS Google Analytics} h1. Spring-Mass Harmonic Oscillator in MATLAB Consider a spring-mass system shown in the figure below. \\ \\ [!spring_mass.png|width=350!|^spring_mass.png]\\ \\ Applying _F = ma_ in the x-direction, we get the following differential equation for the location x(t) of the center of the mass: {latex} \[ m \ddot{x} + k x =0 \] {latex} |
The
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initial
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conditions
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at
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t=0
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are
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{latex}
\[
x(0)=1,
\]
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and
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{latex} and {latex} \[ v(0)=\dot{x} ̇(0)=0 \] {latex} The first condition above specifies the initial location _ |
The first condition above specifies the initial location x(0)
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and
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the
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second
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condition,
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the
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initial
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velocity
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v(0)
...
.
We’ll solve this differential equation numerically, i.e.
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integrate
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it
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in
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time
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starting
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from
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the
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initial
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conditions
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at
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t=0,
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using
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MATLAB.
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We’ll use
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Euler's
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method
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to
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perform
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the
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numerical
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integration. Some other topics covered in this tutorial are:
- Making a plot of mass position vs. time and comparing it to the analytical solution
- Separating out the Euler's method in a MATLAB "function"
- Collecting multiple parameters in one box using "structures"
In the process, you'll be exposed to the following handy MATLAB utilities:
- Debugger to understand and step through code
- Code analyzer to check code
- Profiler to time code