I tried looking this up and I didn't see anything that addressed this:


Let's suppose you're holding one end of a freely hanging rope.
Then you start to give it some rotation by revolving the part you're holding
around the y-axis.
Get it going so that you're twirling it around (it will happen at a harmonic
frequency) and it curves outward [the free end likely crossing over the y-axis].

I was just idly wondering if the shape of that curve would be a catenary.
 ... and if it's the same curve that results from imparting a simple harmonic
motion to it in a plane while it's dangling freely.

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