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spring_ode2.html
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<html>
<head>
<title>
SPRING_ODE2 - Gnuplot Graphics to Display Spring ODE Solution
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPRING_ODE2 <br> Gnuplot Graphics to Display Spring ODE Solution
</h1>
<hr>
<p>
<b>SPRING_ODE2</b>
is a MATLAB program which
shows how Gnuplot graphics can be used to illustrate a solution of
the ordinary differential equation (ODE) that describes the motion
of a weight attached to a spring.
</p>
<p>
This program is a revision of the SPRING_ODE program. A second
change that we make is that we use vectors to store the
data.
</p>
<p>
Hooke's law for a spring observes that the restoring force is
proportional to the displacement:
<pre>
F = - k x
</pre>
and Newton's law relates the force to acceleration:
<pre>
F = m a
</pre>
</p>
<p>
Putting these equations together, we have:
<pre>
m * d^2 x/dt^2 = - k * x
</pre>
</p>
<p>
We can add a damping force with coefficient c:
<pre>
m * d^2 x/dt^2 = - k * x - c * dx/dt
</pre>
If we write this as a pair of first order equations for (x,v), we have
<pre>
dx/dt = v
m * dv/dt = - k * x - c * v
</pre>
and now we can approximate these values for small time steps.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SPRING_ODE2</b> is available in
<a href = "../../c_src/spring_ode2/spring_ode2.html">a C version</a> and
<a href = "../../cpp_src/spring_ode2/spring_ode2.html">a C++ version</a> and
<a href = "../../f77_src/spring_ode2/spring_ode2.html">a FORTRAN77 version</a> and
<a href = "../../f_src/spring_ode2/spring_ode2.html">a FORTRAN90 version</a> and
<a href = "../../m_src/spring_ode2/spring_ode2.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/flame_ode/flame_ode.html">
FLAME_ODE</a>,
a MATLAB library which
considers an ordinary differential equation (ODE) which models
the growth of a ball of flame in a combustion process.
</p>
<p>
<a href = "../../examples/gnuplot/gnuplot.html">
GNUPLOT</a>,
examples which
illustrate the use of the gnuplot graphics program.
</p>
<p>
<a href = "../../examples/graphics_examples_gnuplot/graphics_examples_gnuplot.html">
GRAPHICS_EXAMPLES_GNUPLOT</a>,
gnuplot scripts which
illustrate how various kinds of data can be displayed and analyzed graphically
using the interactive executable graphics program GNUPLOT.
</p>
<p>
<a href = "../../m_src/spring_ode/spring_ode.html">
SPRING_ODE</a>,
a MATLAB program which
shows how line printer graphics can be used to make a crude illustration
of a solution of the ordinary differential equation (ODE) that describes
the motion of a weight attached to a spring.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "spring_ode2.m">spring_ode2.m</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "spring_ode2_output.txt">spring_ode2_output.txt</a>,
the output file, which contains just the graphics data.
</li>
<li>
<a href = "xv_time.png">xv_time.png</a>,
a time plot, created by gnuplot, of the displacement x and velocity v.
</li>
<li>
<a href = "xv_phase.png">xv_phase.png</a>,
a phase plot, created by gnuplot, of the displacement x and velocity v.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 27 June 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>