## Mathematics & Science
Learning Center |
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## Applications of Differential Equations## The Simple Pendulum
Your picture should look like this, this time: Don't misinterpret what you are seeing here in the picture. The
red graph shows Let's discuss the implication of these two totally different looking functions: -
It looks like the **actual**pendulum (the upper, red graph) makes an angle with the equilibrium position,*y*= 0, that just keeps on increasing forever. Physically this means that the pendulum**just keeps spinning in a circle**, generating a larger and larger positive angular displacement. -
On the other hand, (don't be fooled by your instincts,) the **linearized**model (the blue graph) gives a totally unbelievable solution! It shows a positive displacement of as high as 3.2 radians at first (that's), but then it actually*more than 180 degrees***comes back**and does a similar displacement in the opposite direction. It repeats this forever. Think about it—this is physically impossible.
Now you may say that the actual solution is
impossible too—after all, a real pendulum can't just keep spinning forever.
However, remember, our pendulum model is frictionless, so in theory We now move on to consider a more realistic model for the pendulum... |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |