- #1
- 23,274
- 5,678
Another member and I, in private conversations, have been discussing the time average tension in a pendulum string. He has done a numerical analysis of the problem, and his calculations indicate that the time average tension is less than mg. I have analyzed the problem analytically by expanding in the maximum angle ##\theta_0## for small values of this angle and found that the time average tension, at least for small maximum angles, is ##mg\left(1+\left(\frac{\theta_0}{2}\right)^2\right)##; so my analysis suggests that the time average tension is greater than mg. I'd like to give other members a chance to weigh in on this.
The parameters are: string length = L, mass = m, maximum angle with vertical = ##\theta_0##.
The parameters are: string length = L, mass = m, maximum angle with vertical = ##\theta_0##.