This reminded me of an old physics problem from my undergraduate days. From McGill, David J., and Wilton W. King. Engineering Mechanics, An Introduction to Dynamics. 2nd ed. Boston: PWS-Kent Pub., 1989. Print.
From Chapter 4: Kinetics of Rigid Body in Plane Motion/Differential Equations Governing Motion Problem 4.69
Agrees with book's answer (yeah!):
Illustrated Audio book with captions, if you don't recognize literary reference:
From 1961 Vincent Price version "Pit and the Pendulum":
As we remember #VincentPrice on his birthday here's a great scene from THE PIT AND THE PENDULUM! http://t.co/OzzjSLu6Hs— PoeForevermore (@PoeForevermore) May 27, 2015
From the above film clip, it doesn't look the assumptions for my calculations are correct because the pin certainly doesn't look frictionless.
In case you've never heard of the author, a Poe biography from "Poe, Edgar Allan." Grolier Encyclopedia. Vol. 8. New York: Grolier Society, 1954. 380-381. Print.
Ahh that comforting, musty book smell... Love letters to libraries: Jacqueline Wilson http://t.co/YtvSWOsvzM— Suzie Brzezinska (@Suze422) November 27, 2014
I'm really skeptical of the veracity of the above article that Poe's last words were "Lord, help my poor soul."
And in case you wondered what was the deep philosophical meaning of a swinging pendulum, MIT open course lecture on Douglas R Hofstadter's book "Gödel, Escher, Bach: An Eternal Golden Braid" gives you the answer @29:53: