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

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.
  • #1
SigmaCrisis
15
0
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.
 
Physics news on Phys.org
  • #2
Not quite period goes as sqrt{L} i.e increasing the length by 4 increases the period by 2
 
Last edited:
  • #3
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.
 

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

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.

Similar threads

  • Introductory Physics Homework Help
Replies
14
Views
562
  • Introductory Physics Homework Help
Replies
27
Views
825
  • Introductory Physics Homework Help
Replies
9
Views
837
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
833
  • Introductory Physics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Back
Top