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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.
The equation is T = 2â¢Ïâ¢(m/k).5 where T is the period, m is the mass of the object attached to the spring, and k is the spring constant of the spring. The equation can be interpreted to mean that more massive objects will vibrate with a longer period.Their greater inertia means that it takes more time to complete a cycle.he spring constant (k in the Hooke's law equation) is the ratio of the F/x. If this ratio is low, then there will be a relatively large displacement for any given F value. Being displaced furthest from the equilibrium position will set the spring into a relatively high amplitude vibrational motion.