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1. The problem statement
Hi everyone, I'm currently working on an assignment that involves modelling a non-linear pendulum in C. I have to investigate the dynamics of a simple non-linear pendulum all the way up to a chaotic damped, driven situation. However, I'm completely baffled as to how to find the frequency of oscillation and period through my simulation (for large amplitudes). Do I simply use a counting method which involves storing the times at which the pendulum angle (or angular velocity) change sign, or is there some other more efficient method? I'm not asking for code, I just want some guidance as to what course of action to take.
For the moment, I'm modelling the simple non-linear pendulum with equation:
[itex]\frac{d^{2}θ}{dt^{2}}[/itex] = -[itex]\frac{g}{l}[/itex]sinθMy Runge-Kutta code is based on the following equations:
[itex]\frac{dθ}{dt}[/itex] = ω
[itex]\frac{dω}{dt}[/itex] = -[itex]\frac{g}{l}[/itex]sinθ
ω = angular velocity
g = acceleration due to gravity
l = length of pendulum
θ = angle of pendulum in relation to the vertical
Hi everyone, I'm currently working on an assignment that involves modelling a non-linear pendulum in C. I have to investigate the dynamics of a simple non-linear pendulum all the way up to a chaotic damped, driven situation. However, I'm completely baffled as to how to find the frequency of oscillation and period through my simulation (for large amplitudes). Do I simply use a counting method which involves storing the times at which the pendulum angle (or angular velocity) change sign, or is there some other more efficient method? I'm not asking for code, I just want some guidance as to what course of action to take.
Homework Equations
For the moment, I'm modelling the simple non-linear pendulum with equation:
[itex]\frac{d^{2}θ}{dt^{2}}[/itex] = -[itex]\frac{g}{l}[/itex]sinθMy Runge-Kutta code is based on the following equations:
[itex]\frac{dθ}{dt}[/itex] = ω
[itex]\frac{dω}{dt}[/itex] = -[itex]\frac{g}{l}[/itex]sinθ
ω = angular velocity
g = acceleration due to gravity
l = length of pendulum
θ = angle of pendulum in relation to the vertical
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