Animations

Here you can find the gnuplot scripts for most of the animations that I showed you in the class. They are in the form of tar gzipped archives. Most of the archives contain two files. After extracting them to any directory of your choice, you can run the animation by typing

gnuplot initxyz.plt

Feel free to experiment by editing the parameter values. I have been a bit too lazy to put in comments about what each and every parameter means - but you should be able to figure that out.

A more serious omission on my part is that most of these animations run over infinite loops - so the way to stop them is to hit Ctrl-C at the command prompt. Unfortunately, in most systems, gnuplot runs by default in the "always in front" mode - which means that the focus is always on the plot window - rather than the terminal. In my Debian system I have seen that hitting "q" kills the plot window (which then comes alive immediately!) and then subsequently allows you to transfer focus to the terminal (so that you can hit on Ctrl-C to terminate your gnuplot command)!

  1. SHM as a projection of circular motion.
  2. Animated x versus t plots of a damped harmonic oscillator for a fixed initial condition as the damping increases. Note in particular the smooth transition from underdamped to overdamped oscillations. The blue and green curves correspond to the undamped and critically damped cases, respectively.
  3. Lissajous figures : composition of two SHMs at right angles to each other.
  4. Two coupled oscillators obeying the equation of motion

    Change the initial conditions to experiment!
  5. Collective oscillations of a monoatomic chain of N atoms with periodic boundary conditions. The animation plots two normal modes by default. The parameters m1 and m2 denote the modes.
  6. Waves of a string for various boundary conditions animated by using the d'Alembert solution u(x,t) = f(x-ct)+g(x+ct) . This archive has six different animations (twelve files!) :
    1. Waves on an infinite string
    2. Waves on a semi-finite string - look out for the reflection at x=0!
      1. End at x = 0 fixed
      2. End at x = 0 free
    3. Waves in a string fixed at both ends.
    4. Reflection and transmission of a wave as it travels from one string to another.
    5. Multiple reflection-transmissions in a composite string.
  7. Fourier sums for square and triangular waves
  8. Animation showing waves in a plucked string fixed at both ends by summing the Fourier series.
  9. Animation showing waves in a plucked string fixed at both ends in the presence of damping by summing the Fourier series.
  10. Convolution of two functions.
  11. Phase and group velocity of a wavepacket
  12. Dispersion of a Gaussian wavepacket where the dispersion relation is . Incidentally, this is the way in which a Gaussian wave packet describing a free particle in quantum mechanics will evolve. Note the spreading of the wave packet as time goes by.
  13. Light polarization : note the change in shape of the polarization ellipse as well as the sense of rotation as the phase difference between the two components change.