Differential equation for motion of a pendulum

AI Thread Summary
The discussion focuses on modeling pendulum motion in Matlab, incorporating non-linear components like friction. The equation of motion presented is \ddot{\phi}(t) = -k_2\dot{\phi}(t) - k_3\sin(\phi(t)). To achieve a sinusoidal solution, the common approach is to linearize the equation by assuming small angles, replacing sin(φ(t)) with φ(t). This simplification allows for easier analysis and fitting of the measured curve. The conversation emphasizes the need for adjustments to the equation to align with the desired sinusoidal output.
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:
\ddot{\phi}(t) = -k_2\dot{\phi}(t)-k_3\sin(\phi(t))

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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