Differential equation for motion of a pendulum

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SUMMARY

The discussion focuses on modeling pendulum motion using a differential equation in Matlab, specifically addressing the equation of motion: \(\ddot{\phi}(t) = -k_2\dot{\phi}(t) - k_3\sin(\phi(t))\). The user seeks to modify this equation to achieve a sinusoidal solution, while also considering non-linear components such as friction. The common approach suggested involves linearizing the equation by approximating \(\sin(\phi(t))\) with \(\phi(t)\) under the assumption of small angle swings.

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Students and researchers in physics and engineering, particularly those interested in mechanical systems, pendulum dynamics, and numerical modeling in Matlab.

fiso
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Hello,

I'm trying to create a model of pendulum motion in Matlab to fit the curve we measured in class, and it has some non-linear components (friction). It looks like the best fit is a sinusoid with an envelope given by a parabola (see attached file).

The equations of motion are given by:
[itex]\ddot{\phi}(t) = -k_2\dot{\phi}(t)-k_3\sin(\phi(t))[/itex]

How this equation can be changed so that the solution of it is a searched sinusoid?

Thank you.

// edit: please move this to Differential Equations
 

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The usual approach is to linearize, assuming the angle of the swing is small, so replace sin(φ(t)) by φ(t).
 

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