Relationship between Period of a pendulum and length

In summary, the formula to find the period of a pendulum is t=2pi √ L/g, where pi=3.14, L is the length of the pendulum, and g is gravity. The equation for simple harmonic motion can be written as sin \theta ~= \theta, and this can be used as a small angle approximation when the angle is small.
  • #1
Dynamite
28
0

Homework Statement



The formula to find the period of a pendulum is t=2pi √ L/g
where pi = 3.14...
L=length of pendulum
g=gravity

So I was wondering how all of this was put together. How they related together? Why it is multiplied by 2pi

The Attempt at a Solution


I really don't know, it's I'm asking here. I tried graphing it and it gives me a curve.
 
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  • #2
Hint: Write the equation for simple harmonic motion in terms of [itex]\theta[/itex]
 
  • #3
And use a small angle approximation. That is:

[tex] sin \theta ~= \theta [/tex]

This is applied when an angle is pretty small.
 
  • #4
thank you!
 

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

The period of a pendulum is directly proportional to the square root of its length. This means that the longer the length of the pendulum, the longer its period will be. Conversely, a shorter pendulum will have a shorter period.

2. How does mass affect the relationship between period and length of a pendulum?

The mass of a pendulum does not affect the relationship between period and length. As long as the length remains constant, the period will not be affected by the mass of the pendulum.

3. Can the relationship between period and length of a pendulum be applied to all pendulums?

The relationship between period and length is only applicable to simple pendulums, which are pendulums with a small swinging mass and a weightless string. Complex pendulums, such as those with a large swinging mass or a rigid rod, have different relationships between period and length.

4. How does gravity affect the relationship between period and length of a pendulum?

The relationship between period and length of a pendulum is affected by gravity. A higher gravitational force will result in a shorter period, while a lower gravitational force will result in a longer period. However, for small oscillations, this effect is minimal and can be ignored.

5. Is the relationship between period and length of a pendulum affected by the angle of release?

The angle of release does not affect the relationship between period and length of a pendulum. As long as the length remains constant, the period will not be affected by the angle of release. However, the amplitude (maximum angle of swing) will be affected by the angle of release.

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