0
$\begingroup$

With my lanyard in hand (weighted by my keys), a gentle swinging motion will put the keys in pendulum motion, swinging back and forth. Pendulum motion is relatively easy to model since it is sinusoidal. With a more forceful swing, the keys on the will instead travel in a circular motion. Circular motion can also be modeled sinusoidally.

If I swing my lanyard with medium power, it will start to take the path of a circle, but before the keys can reach maximum height, they begin to fall and start to model parabolic motion instead. I do not know how to model the path of my keys on my lanyard in this situation. I know it will transition from circular to parabolic motion once the vertical component of the velocity goes under zero, but I don't know what equation I could use. Any help?

$\endgroup$

closed as unclear what you're asking by Carl Witthoft, Gert, user36790, Kyle Kanos, ACuriousMind Feb 5 '16 at 14:38

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ "Sinusoidal" refers to position vs. time. "Circular" refers to x vs. y position in space. Your question is extremely poorly formulated. $\endgroup$ – Carl Witthoft Feb 4 '16 at 20:30
  • $\begingroup$ This is a related, and possible duplicate of this question. $\endgroup$ – fibonatic Feb 5 '16 at 10:46
1
$\begingroup$

Note that pendulum motion is only sinusoidal for small angular displacements; as you increase the amount of swing the harmonic approximation fails.

Lagrangian mechanics gives you a handle on all of the cases.

$\endgroup$
  • $\begingroup$ Hi Peter, this is a comment not an answer $\endgroup$ – John Rennie Feb 5 '16 at 6:40
  • $\begingroup$ This is exactly how I would answer a student asking this question. It is up to them to clarify their thoughts. $\endgroup$ – Peter Diehr Feb 5 '16 at 12:27
  • $\begingroup$ It's a very sparse post, to be sure, but it doesn't seem so obviously not-an-answer as to be deleted. $\endgroup$ – David Z Feb 5 '16 at 14:45

Not the answer you're looking for? Browse other questions tagged or ask your own question.