Pendulum length to falling body height ratio?


How long does a pendulum need to be for its time period to be equal to the time it takes for a falling body to drop from a distance equal to the pendulum's length? A general equation as well as a specific solution for Earth surface gravity would be appreciated. With this, I would be able to establish standard time and distance units even if trapped on an island without any instruments other than what I can make from available materials. I'm sure I'm the only one tired that happening so often. Of course, I'd still need a way to establish the gravitatoinal constant if stranded on another planet...

kelseymh7 years ago
Did you know that you can get both expressions from Wikipedia? Look up "pendulum" and "gravity". Use the small angle approximation for the pendulum to keep things simple. The rest is just algebra, but you're going to be disappointed with the result.