spring_ode2/spring_ode2.html

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    <title>
      SPRING_ODE2 - Gnuplot Graphics to Display Spring ODE Solution
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      SPRING_ODE2 <br> Gnuplot Graphics to Display Spring ODE Solution
    </h1>

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    <p>
      <b>SPRING_ODE2</b>
      is a C++ 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 (C arrays) 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>

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      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>

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      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 = "../../cpp_src/gnuplot/gnuplot.html">
      GNUPLOT</a>,
      C++ programs which
      illustrate the use of the gnuplot graphics program.
    </p>

    <p>
      <a href = "../../cpp_src/lorenz_ode/lorenz_ode.html">
      LORENZ_ODE</a>,
      a C++ program which
      approximates solutions to the Lorenz system,
      creating output files that can be displayed by Gnuplot.
    </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 = "../../cpp_src/spring_ode/spring_ode.html">
      SPRING_ODE</a>,
      a C++ 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.cpp">spring_ode2.cpp</a>, the source code.
        </li>
        <li>
          <a href = "spring_ode2.sh">spring_ode2.sh</a>,
          BASH commands to compile the source code.
        </li>
      </ul>
    </p>

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      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "spring_ode2_output.txt">spring_ode2_output.txt</a>,
          the output file.
        </li>
        <li>
          <a href = "spring_ode2_data.txt">spring_ode2_data.txt</a>,
          the graphics data file.
        </li>
        <li>
          <a href = "spring_ode2_commands.txt">spring_ode2_commands.txt</a>,
          the graphics command file.
        </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>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>MAIN</b> is the main program for SPRING_ODE2.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../cpp_src.html">
      the C++ source codes</a>.
    </p>

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    <i>
      Last revised on 09 October 2013.
    </i>

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