okay i have a question about pendulum swings.?

Question

A pendulum swings back and forth with a period of 0.5 s. what is the lenght of the pendulum arm?
somebody please help i just started this yesterday and really don't understand.

Answer 1

The length L is given by L = 0.06206... m = 6.206 cm. Why? :

The period of a pendulum P (the time for one complete swing back and forth) is given by:

P = 2 pi sqrt (L/g), where L is the length of the pendulum arm and ' g ' is the acceleration due to gravity where the pendulum is --- usually at the Earth's surface.

Rearranging this relationship,

P^2 = 4 (pi)^2 L / g, so that L = g P^2 / [4 (pi)^2].

So, in this case, L = (9.8) (0.5)^2 / [4 (pi)^2] metres

= 0.06206... m = 6.206 cm.

Live long and prosper.