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The equation for the period of a simple pendulum starting at a small angle (a) is: T = 2pi*SQRT(L/g). or. T = 2Ïâ(L/g). where. 1  T is the period in seconds (s). 2  pi = 3.14 (it is also written as the Greek letter Ï).quations for period and frequency. The period of the motion for a pendulum is how long it takes to swing back-and-forth, measured in seconds. Period is designated as T. The frequency of a pendulum is how many back-and-forth swings there are in a second, measured in hertz. Frequency is usually designated as f.
For comparison of the approximation to the full solution, consider the period of a pendulum of length 1 m on Earth (g = 9.80665 m/s 2) at initial angle 10 degrees is.he motion is simple harmonic motion where Î¸ 0 is the semi-amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical). The period of the motion, the time for a complete oscillation (outward and return) is. which is known as Christiaan Huygens 's law for the period.