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Simulating a Simple Pendulum in Python

Post to Cancel. If we assume zero friction at the top mount of the pendulum, no atmospheric drag, and a stiff pendulum arm, this problem can be modeled with a relatively simple mathematical equation. Expanding about , gives, to the first order:. While we have seen several ways to go about this type of problem, in this instance lets compute all the array elements as we go through the loop e. Like Like. Numerical Algorithm Our next step is the construction of an algorithm that tells us how to update the dependent variables in the problem. In the case of a simple pendulum, I could tell them the and positions of the mass, of course, but I could also just tell them the angle the pendulum makes with the vertical.
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Simulating a Simple Pendulum in Python | Jeremy Kao

In lieu of using higher-order methods, we can just apply a simple modification called the Euler-Cromer method , which is guaranteed to conserve energy. In this case we also have an analytic solution to compare with, at least in the limit that the pendulum angle remains small. At this stage, many introductory physics courses will take the small-angle approximation in order to obtain the equation for simple harmonic motion , which can be solved analytically. A schematic of a simple pendulum is presented below:.
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Description: If we assume zero friction at the top mount of the pendulum, no atmospheric drag, and a stiff pendulum arm, this problem can be modeled with a relatively simple mathematical equation. Sections of this page. In this current problem we are calculating the motion for many dynamical times, allowing the errors to build up to noticable proportions. The kinetic energy is easily written by remembering the relation for circular motion and noting that in our case, the radius is simply the length of the pendulum:. Sign Up.

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Views: 5079 Date: 10.07.2019 Favorited: 5 favorites

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