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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} {note} If you get a "LaTex markup" error on this page, please reload the page to see the equations that use the Latex markup. {note} 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
...
are
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{latex} \[ x(0)=1, \] {latex |
and
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} 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)
...
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)
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.
We’ll solve this differential equation numerically, i.e.
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integrate
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it
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in
...
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
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other
...
topics
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covered
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in
...
this
...
tutorial
...
are:
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- Making
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- a
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- plot
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- of
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- mass
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- position
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- vs.
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- time
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- and
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- comparing
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- it
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- to
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- the
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- analytical
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- solution
...
- Separating
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- out
...
- the
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- Euler's
...
- method
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- in
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- a
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- MATLAB
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- "function"
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- Collecting
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- multiple
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- parameters
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- in
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- one
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- box
...
- using
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- "structures"
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In
...
the
...
process,
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you'll
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be
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exposed
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to
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the
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following
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handy
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MATLAB
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utilities:
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- Debugger
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- to
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- understand
...
- and
...
- step
...
- through
...
- code
...
- Code
...
- analyzer
...
- to
...
- check
...
- code
...
- Profiler
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- to
...
- time
...
- code