Coverting Simple Harmonic Motion Equation to a Rotational Model

[james6008]

Hi

I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass.

A perpendicular force is applied to this object and it rotates around that pivot point (moving left and right only). The pendulum model considers the gravity while this is not affected by gravity at all.

I wanted to know if there is a way I can make use of Simple Harmonic Motion to calculate the change in rotational angle (from initial condition where it is 0 degrees) when a perpendicular force is applied to this object. The maximum it can move is 90 degrees on either direction.

How can I use the calculated acceleration & velocity from the model to represent this angular change?

 

[T2theB]

Is your object the balance wheel of a mechanical watch?

I asked because what you described sounds quite similar to an article I read in an IEEE publication about whether a tourbillion escapement has a real impact on the accuracy and precision of a watch's movement. I believe there were some formulas in that article that may address what you seek. If so, let me know and I'll try to dig up that article.

All the best.