Yes.
The derivation of the simple formula for the period of the pendulum requires the angle, theta (in radians) to be small so that sin(theta) and theta are approximately equal. There are more exact formulae, though.
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Height does not affect the period of a pendulum.
The period of a pendulum is affected by the angle created by the swing of the pendulum, the length of the attachment to the mass, and the weight of the mass on the end of the pendulum.
A longer pendulum will have a smaller frequency than a shorter pendulum.
The period of the pendulum is unchanged by the angle of swing. See link.
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.