What is the relationship between the period and length of a pendulum?

[SigmaCrisis]

I have this question:

You are doing some spring cleaning and decide to clean out your house. You want to make a new window in your wall with which to see nature come to life, so you tie a heavy mass to a short string and attach the string to a beam in your ceiling so it can swing freely like a pendulum. You lift the ball and let it go for practice, and it takes exactly 0.5 s to come right back to you. Ready for the real thing, you quadruple the length of the pendulum. Were it to swing freely also, it would take ____ s to return to you after you let it go.


So I went over the equation for a period quite a few times and tested a few calculations to make sure and finally concluded that the period would be quadrupled if the length is quadrupled.

The equation for a period is (in the book):

period of a pendulum = 2(pi) * ((sqrt)(length of pendulum/acceleration due to gravity))

Was my conclusion right? My answer was 2 seconds.

 

[drcrabs]

Not quite period goes as sqrt{L} i.e increasing the length by 4 increases the period by 2

 

[SigmaCrisis]

Not quite period goes as sqrt{L} i.e increasing the length by 4 increases the period by 2

Got it. I'm dumb, and very sleepy.