The period of a pendulum is give approximately by the formula
t = 2*pi*sqrt(l/g) where l is the length of the pendulum and g is the acceleration (not accerlation) due to gravity. Thus g is part of the formula for the period.
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Yes. Given a constant for gravity, the period of the pendulum is a function of it's length to the center of mass. In a higher gravity, the period would be shorter for the same length of pendulum.
Height does not affect the period of a pendulum.
The period of a pendulum (in seconds) is 2(pi)√(L/g), where L is the length and g is the acceleration due to gravity. As acceleration due to gravity increases, the period decreases, so the smaller the acceleration due to gravity, the longer the period of the pendulum.
It messes up the math. For large amplitude swings, the simple relation that the period of a pendulum is directly proportional to the square root of the length of the pendulum (only, assuming constant gravity) no longer holds. Specifically, the period increases with increasing amplitude.
For a simple pendulum, consisting of a heavy mass suspended by a string with virtually no mass, and a small angle of oscillation, only the length of the pendulum and the force of gravity affect its period. t = 2*pi*sqrt(l/g) where t = time, l = length and g = acceleration due to gravity.