The discussion centers on the conical pendulum's height issue, specifically when the height (h) exceeds the string length (L). It is established that the period of the conical pendulum, given by the formula T=2π√(h/g), must be less than that of a planar pendulum, which is approximately 3.5 seconds for a 3m string. The critical condition for the conical pendulum's existence is Lω² ≥ g; otherwise, the radius becomes zero or imaginary. The conversation highlights the importance of correctly specified values for real solutions in pendulum problems.
PREREQUISITESPhysics students, educators, and anyone interested in the mechanics of pendulums and circular motion dynamics.
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:
