the law of pendulums

after playing with pendulums, children discover that the length is an important variable in determining its frequency.

below is a diagram showing exactly how the length of the pendulum relates to its frequency. Analyze the data and see if you can derive "the empirical law of pendulum frequency."

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would the weight of the pendulum bob alter the rate ?
would the width of the swing ( amplitude ) alter it ?
would pushing the pendulum change it ?

comparing the length and the frequency

64 units long and --- 10 tic tocks
32 units long and --- 14 tic tocks
16 units long and --- 20 tic tocks
7.1 units long and -- 30 tic tocks
4 units long and ---- 40 tic tocks

analysis

gads -- it goes . . .

1.4x faster ( 14 tic tocks vs. 10 tic tocks ) if i cut the string by ______

2x faster ( 20 tic tocks vs 10 tic tocks ) if i cut the string by ______

3x faster ( 30 tic tocks vs 10 tic tocks ) if i cut the string by ______

4x faster ( 40 tic tocks vs 10 tic tocks ) if i cut the string by ______

so what is the law of pendulums ? How do you make it go 5x faster ?

Remember the playground swing ? What if the chain on the swing was four times longer than a pendulum in your hand ?
What are the relative speeds of the two pendula ? 10/24t/95 -- 4/19f/96