This problem is actually a simplification of something seen in a data visualization tool.(adsbygoogle = window.adsbygoogle || []).push({});

I think it is interesting in that it can be "translated" to a Hooke's Law problem.

Unfortunately, I am not sure how to proceed...

Suppose I have a point mass tethered to several springs. The springs are attached in a co-circular fashion to a rigid metal ring. The springs are equidistant from each other on the circular ring. The point mass is at some equilibrium position inside the ring.

Now, suppose we are able to slide one (and only one!) of the springs around the metal ring.

All the way around the circle.

How would you describe the movement of the point mass inside the ring? At first it seems that the point mass would move strictly in a circle of some varying radius. Instead what I am seeing from my software (in some cases) is that the point mass traces an elliptical path.

Why is that? I assume I haven't made some sort of coding error!

The position of the point mass when we start is for M springs

([itex]\sum_{j=0}^{M-1}[/itex] cos [itex]\Theta_j[/itex] * k[itex]_{j}[/itex], [itex]\sum_{j=0}^{M-1}[/itex] sin [itex]\Theta_{j}[/itex] * k[itex]_{j}[/itex] )

If we then move one of the springs to some new position (say it is the first spring)

The position is now

([itex]\sum_{j=1}^{M-1}[/itex] cos [itex]\Theta_j[/itex] * k[itex]_{j}[/itex] + [itex]\sum_{j=0}^{0}[/itex] cos [itex]\Theta_j[/itex] * k[itex]_{j}[/itex], [itex]\sum_{j=1}^{M-1}[/itex] sin [itex]\Theta_{j}[/itex] * k[itex]_{j}[/itex] + [itex]\sum_{j=0}^{0}[/itex] sin [itex]\Theta_{j}[/itex] * k[itex]_{j}[/itex])

This still seems to describe a circle to me. If we pick any spring (not just the first as in the example) and move it a full 360Â° I still only intuit a circular path.

Any advice and corrections would be appreciated!

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# Action of co-circular springs on a point mass

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