For small angles, the formula for a pendulum's period (T) can be approximated by the formula:
T = 2 * pi * sqrt(L/g), where L is the length of the pendulum length, and g is acceleration due to gravity. See related link for Simple Pendulum.
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T=1/2l
There's no relationship between the length of the pendulum and the number of swings.However, a shorter pendulum has a shorter period, i.e. the swings come more often.So a short pendulum has more swings than a long pendulum has in the same amountof time.
The relationship between log(period) and log(length) is linear, with slope 0.5 and intercept log(2*pi/sqrt(g))
You measure the period of the pendulum for different lengths. Plot the results on a scatter plot and see if you can work out the nature of the relationship between the two variables.
t = 2*pi*sqrt(l/g) Where t is the period, l is the length and g is the accelaration due to gravity.