- #1

roobs

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I know you do it by rearranging this equation T = 2π√(L/g).

But how exactly do you prove that equation??

just curious...

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- Thread starter roobs
- Start date

In summary: Galileo claimed that the period of a pendulum is not dependent on the amplitude of the swing, but this was later found to be wrong.

- #1

roobs

- 6

- 0

I know you do it by rearranging this equation T = 2π√(L/g).

But how exactly do you prove that equation??

just curious...

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- #2

granpa

- 2,268

- 7

I don't know what your teacher wants but

the way that I would do it is to approximate the pendulum with a mass spring system.

The equations for a mass spring system are pretty easy.

You should be aware though that a pendulum doesn't perfectly resonate.

The restoring force isn't perfectly linear.

But for very small angles it approaches quite closely to it.

http://en.wikipedia.org/wiki/Simple_harmonic_motion#Mass_on_a_simple_pendulum

the way that I would do it is to approximate the pendulum with a mass spring system.

The equations for a mass spring system are pretty easy.

You should be aware though that a pendulum doesn't perfectly resonate.

The restoring force isn't perfectly linear.

But for very small angles it approaches quite closely to it.

http://en.wikipedia.org/wiki/Simple_harmonic_motion#Mass_on_a_simple_pendulum

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- #3

roobs

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I know... but i am asking how we can prove this T = 2π√(L/g)

- #4

Dadface

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roobs said:I know... but i am asking how we can prove this T = 2π√(L/g)

What have you tried and where are you stuck?

- #5

granpa

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I answered your question and

I also pointed out that

your equation is only an approximation

I also pointed out that

your equation is only an approximation

- #6

roobs

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Dadface said:What have you tried and where are you stuck?

ermm...i do not know where to start yet

just tell me in words what that equation mean and how to prove it, no need for working out

Thanks

- #7

granpa

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http://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics_of_simple_harmonic_motion

- #8

Dadface

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roobs said:ermm...i do not know where to start yet

just tell me in words what that equation mean and how to prove it, no need for working out

Thanks

As granpa pointed out the equation is an approximation only but it works well provided that the amplitude of swing is small.The equation relates the time period(T) which is the time taken for one complete swing of the pendulum to the length(L) of the pendulum.g is the acceleration due to Earth's gravity.

- #9

granpa

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what class is this for

how much do you know about simple harmonic motion?

Have you done simple mass/spring systems yet?

You should do those before you try to do pendulums.

- #10

roobs

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Also, is it safe to say that the mass of the pendulum and the angle at which it is released does not change the period (assuming no air resistance and friction)?

I am a high school physics student and i have done mass/spring systems

- #11

granpa

- 2,268

- 7

http://en.wikipedia.org/wiki/Pendulum#Period_of_oscillation

which for small angles is approximately:

which for small angles is approximately:

- #12

roobs

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but some sites say the period is not dependent on the initial amplitude, such as this one

http://muse.tau.ac.il/museum/galileo/pendulum.html

which stated " Galileo examined a variety of pendulums and claimed that the period of each is totally independent of the size of the arc through which it passes. A pendulum with an angle of 80 degrees has an identical period to that of a pendulum with an angle of 2 degrees."

- #13

roobs

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okay i get most of this now

thanks a lot for the replies

The length of the pendulum does not affect the gravitational acceleration. The gravitational acceleration is determined by the mass of the Earth and the distance between the pendulum and the center of the Earth, not the length of the pendulum.

Yes, the gravitational acceleration can be calculated using only the period of the pendulum. The equation for calculating gravitational acceleration with a pendulum is g = 4π²L/T², where g is the gravitational acceleration, L is the length of the pendulum, and T is the period of the pendulum.

The mass of the pendulum does not affect the gravitational acceleration. As long as the mass of the pendulum is much smaller than the mass of the Earth, it will have a negligible effect on the gravitational acceleration.

Yes, gravitational acceleration can be calculated with any type of pendulum as long as the length and period of the pendulum are accurately measured. However, it is important to use a pendulum with a small mass compared to the Earth in order to minimize any effects on the gravitational acceleration.

The calculation of gravitational acceleration with a pendulum can be quite accurate, as long as the length and period of the pendulum are measured precisely. However, there may be slight variations due to external factors such as air resistance or the mass of the pendulum itself.

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