spring_ode/spring_ode.html

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    <title>
      SPRING_ODE - Line Printer Graphics to Display Spring ODE Solution
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      SPRING_ODE <br> Line Printer Graphics to Display Spring ODE Solution
    </h1>

    <hr>

    <p>
      <b>SPRING_ODE</b>
      is a FORTRAN90 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>

    <p>
      This is a simple example of how to plot when you don't have a plotter.
      This is a particular kind of "ASCII graphics", or "typewriter graphics"
      or "lineprinter graphics", and shows you how valuable an illustration 
      can be, even when it's as crude as this example.
    </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>

    <p>
      Note that the plotting assumes that the value of X will always be
      between -1 and +1.  If the initial condition uses V = 0, and X starts
      between -1 and +1, then this will be OK.
    </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_ODE</b> is available in
      <a href = "../../c_src/spring_ode/spring_ode.html">a C version</a> and
      <a href = "../../cpp_src/spring_ode/spring_ode.html">a C++ version</a> and
      <a href = "../../f77_src/spring_ode/spring_ode.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/spring_ode/spring_ode.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/spring_ode/spring_ode.html">a MATLAB version</a>.
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../data/ascii_art_grayscale/ascii_art_grayscale.html">
      ASCII_ART_GRAYSCALE</a>,
      a data directory which
      contains examples of grayscale ASCII Art files,
      in which images are created using printable characters.
    </p>

    <p>
      <a href = "../../c_src/mandelbrot_ascii/mandelbrot_ascii.html">
      MANDELBROT_ASCII</a>,
      a C program which
      generates an ASCII TEXT image of the Mandelbrot fractal set
      using just two lines of (very obscure) C.
    </p>

    <p>
      <a href = "../../f_src/spring_ode2/spring_ode2.html">
      SPRING_ODE2</a>,
      a FORTRAN90 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>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "spring_ode.f90">spring_ode.f90</a>, the source code.
        </li>
        <li>
          <a href = "spring_ode.sh">spring_ode.sh</a>,
          BASH commands to compile the source code.
        </li>
        <li>
          <a href = "spring_ode_output.txt">spring_ode_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

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      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>MAIN</b> is the main program for SPRING_ODE.
        </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 = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 15 May 2012.
    </i>

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