How do you calculate gravitational acceleration with a pendulum?

[roobs]

How do you calculate 'g' when the length and the period is known for a pendulum
I know you do it by rearranging this equation T = 2π√(L/g).

But how exactly do you prove that equation??

just curious...:uhh:

[granpa]

I dont 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 doesnt perfectly resonate.
The restoring force isnt 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

http://upload.wikimedia.org/wikipedia/commons/b/b1/Simple_Pendulum_Oscillator.gif
http://upload.wikimedia.org/wikipedia/commons/2/2b/Muelle.gif

[roobs]

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

[Dadface]

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

What have you tried and where are you stuck?

[granpa]

I answered your question and
I also pointed out that
your equation is only an approximation

[roobs]

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

[granpa]

I told you exactly what you need to do.

http://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics_of_simple_harmonic _motion

[Dadface]

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 earths gravity.

[granpa]

how old are you
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.

[roobs]

okay... then is there an equation that is not an approximation??
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

[granpa]

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

http://upload.wikimedia.org/math/3/0/1/3014cdccf9d3df9770a001b84ae6ac80.png

which for small angles is approximately:
http://upload.wikimedia.org/math/5/a/a/5aa04824df4e09c1ae352502bdee9c92.png

[roobs]

wow...okay...you are saying the value of T is different with a small initial angle and a large initial angle
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."

[roobs]

oops...i did not read the next part which said why galileo claims were wrong
okay i get most of this now
thanks a lot for the replies