Re: simple pendulum

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Michael Edmiston wrote:

> However, when solving the conical pendulum, the period's
> dependence upon amplitude is easily seen.
>
> ... Unfortunately I am having trouble equating the two
> [pendula, simple and conical].
>
> The typical equation given for the period of a simple pendulum is
> (2*pi)sqrt(L/g)(1 + (1/4)sin^2(theta/2) + (9/64)sin^4(theta/2) ...)
> i.e. an infinite series.
>
> When I solve the conical pendulum I get that the period is
> (2*pi)sqrt(L/g)sqrt(sec(theta)).
You are correct. What I wrote is true for small angles only. The
claim that the circular motion of the bob of a conical pendulum
is a superposition of two simple pendular motions is NOT valid
in general. The plane and the sphere are different in that respect.

It is easy to verify that for a conical pendulum the angular
dependence of T is more rapid than for the pendulum of the
same length swinging in one plane. Something to think about.

Ludwik Kowalski