The discussion revolves around a conical pendulum problem, specifically addressing the relationship between the height of the pendulum bob and the length of the string. Participants are exploring the implications of given values and their feasibility in the context of the problem.
Participants are actively engaging with the problem, questioning assumptions and exploring the criteria for the conical pendulum's motion. There is a recognition of the need for further validation of the relationships discussed, particularly regarding the periods of different pendulum types.
There are indications that the problem may contain inconsistencies, particularly with the specified height and string length. The discussion includes references to specific criteria that must be met for the conical pendulum to function correctly.
Yes, the period of the conical pendulum is ##T=2\pi \sqrt{\frac{h}{g}}## where ##h## is the "height". Since ##h < L##, it is less than that of the planar pendulum unless, of course, the bob isn't moving.gneill said:
Yes. Circular motion can be decomposed as a superposition of linear harmonic motions at right angles with a 90-degree phase shift. In the limit of small angles for the conical pendulum, the harmonic motions are just pendulum swings of small amplitude which we know have angular frequency ##\sqrt{g/L}##. You cannot make the conical pendulum have a smaller angular frequency than this.gneill said:
