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

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    Pendulum Period
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SUMMARY

The relationship between the period and length of a pendulum is defined by the equation: period = 2π * √(length/g), where 'g' represents the acceleration due to gravity. When the length of the pendulum is quadrupled, the period increases by a factor of 2, resulting in a new period of 2 seconds. This conclusion is based on the principle that the period of a pendulum is proportional to the square root of its length. Therefore, a longer pendulum swings more slowly, confirming the initial calculations presented in the discussion.

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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.
 
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Not quite period goes as sqrt{L} i.e increasing the length by 4 increases the period by 2
 
Last edited:
drcrabs said:
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.
 

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