How do I prove mathematically that only length influences a pendulum's frequency and not mass and amplitude?

Question

ash2326 · Answer

Time period for a pendulum is given as
$$T=2\pi \sqrt{\frac{l}{g}}$$
We know frequency is 1 over time period
$$f=\frac{1}{ T}$$
so
$$f=\frac{1}{2\pi}\sqrt{\frac{g}{l}}$$
We see that mass is not in the relation
Hence frequency is dependent on length of pendulum

anonymous · Answer

how about amplitude?

experimentx · Answer

amplitude does not appear anywhere on the expression of time period of pendulum.
I must say, if amplitude is increased, then it would simply oscillate faster.

jamesj · Answer

Watch this to see the equations worked out in detail: http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-10/ The discussion of pendulums begins at 29:00

anonymous · Answer

woah, thank you :)

mani_jha · Answer

Do you see an amplitude in the expression for Time Period? For a simple pendulum, time period depends only on the length(distance from the point of suspension to the center of mass) and value of 'g'(acceleration due to gravity).
If you don't believe the equation, see it for yourself. Just hang something with a thread, swing it and note the time taken for different amplitudes.