Vibe is a Java-based simulator, but you now have Java turned off. You may turn on Java at any time.
      Harmonic Oscillators:
  Other Categories:
|
  |
   
The Simple Linear Oscillator is ![]() This pendulum adds a sine function which changes the response of the system at its maxima ![]() Note that the 4Pi2 is simply added to keep the time equal to unity, meaning that the oscillator will orbit 1.0 times in 1.0 timesteps.
A ConundrumThe simple pendulum does not preserve periodicity in the same way as the Simple Linear Oscillator. That is, if you start the system with a position of, say, 3 (representing a fairly high-magnitude swing) it will have a markedly slower period than if you start it with a period of, say, 1. The conundrum is this: if the period is varible depending upon how high the pendulum is swinging, how can such a pendulum be used to keep time? After all, if the period of a clock pendulum changes as the mainspring unwinds (lessening amplitude) then shouldn't the clock slow down?Well, yes and no. First, the clock makers try as hard as they can to keep the amplitude of the swing constant by using a mechanism that releases and then catches the pendulum at the same height. The spring powers the pendulum so that it can make it back up to that height again, but there is no gradual degredation in amplitude. But more importantly (at least for our topic) the swing of the pendulum on a clock is of relatively low magnitude. Why is this important? Look at the model. The nonlinearity which makes the Simple Pendulum not a Simple Linear Oscillator is sin(position). This term is vanishingly small as position approaches zero. So with a low-magnitude swing (yielding low-magnitude position values) the nonlinearity is small and the Simple Pendulum acts just like the Simple Linear Oscillator.
|
||
|
Vibe Oscillator Simulator © 2000-2003 Douglas S. Eck. Back to the Vibe Home Page § Back to Douglas Eck's Home Page Thu Jul 24 09:12:34 EDT 2003 |