The period T of a simple pendulum depends
on the length L of the pendulum and the acceleration of
gravity g (dimensions L/T^2). (a) Find a simple combination of
L and g that has the dimensions of time. (b) Check the
dependence of the period T on the length L by measuring
the period (time for a complete swing back and forth) of
a pendulum for two different values of L. (c) The correct
formula relating T to L and g involves a constant that is a
multiple of pi, and cannot be obtained by the dimensional
analysis of Part (a). It can be found by experiment as in
Part (b) if g is known. Using the value g = 9.81 m/s² and your
experimental results from Part (b), find the formula relating T
to L and g.
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