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

• SigmaCrisis
In summary, the conversation discusses the use of a pendulum to determine the period of a swinging motion. The length of the pendulum is directly related to the period, as quadrupling the length would result in a quadrupled period. The equation for the period is also mentioned, and it is clarified that increasing the length by 4 will increase the period by 2.
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.

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.

## 1. What factors affect the period of a pendulum?

The period of a pendulum is affected by the length of the pendulum, the mass of the bob, and the acceleration due to gravity. These factors can be mathematically represented by the equation T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity.

## 2. How does the mass of the bob affect the period of a pendulum?

The mass of the bob does not affect the period of a pendulum. This is because the mass only affects the force of gravity acting on the pendulum, which is already accounted for in the equation for period.

## 3. What is the relationship between the length of a pendulum and its period?

The length of a pendulum and its period have a direct relationship. As the length of the pendulum increases, so does the period. This can be seen in the equation T = 2π√(L/g), where the period is directly proportional to the square root of the length.

## 4. Can the period of a pendulum be affected by air resistance?

Yes, air resistance can affect the period of a pendulum. This is because air resistance creates a force that acts against the motion of the pendulum, causing it to slow down. However, for most pendulum experiments, the effect of air resistance is small and can be ignored.

## 5. How does the angle of release affect the period of a pendulum?

The angle of release does not affect the period of a pendulum. As long as the pendulum is released from the same angle each time, the period will remain constant. However, if the angle of release is changed, the pendulum will follow a different path and the period will be affected.

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