The calculation for the period (T) of a swinging pendulum is defined as T = 2pi*sqr(L/g) where pi is the mathematical constant, L is the length of the arm of the pendulum and g is the acceleration of gravity acting on the pendulum. Examining the equation reveals that the period of oscillation is directly proportional to the length of the arm and inversely proportional to gravity; thus, an increase in the length of a pendulum arm results in a subsequent increase in the period of oscillation given a constant gravitational acceleration. A decrease in length would then result in a decrease in the period. For gravity, the inverse relationship shows that the stronger the gravitational acceleration, the smaller the period of oscillation. For example, the period of a pendulum on Earth would be smaller compared to a pendulum of equal length on the moon.
The calculation for the period (T) of a spring oscillating with a mass (m) is described as T = 2pi*sqrt(m/k) where pi is the mathematical constant, m is the mass hanging from the spring and k is the spring constant. The period of oscillation is, therefore, directly proportional to the mass hanging from the spring and inversely proportional to the spring constant. An increase in the spring constant of the spring with a constant mass results in a decrease in the period of oscillation. Increasing the mass will result in an increase in the period of oscillation.
The period (T) of an oscillating wave particle is the reciprocal of the frequency (f) of the wave as seen in the equation T= 1/f. The equation shows that the period is inversely proportional to the frequency. Therefore, an increase in frequency results in a subsequent decrease in the period of oscillation. A decrease in frequency will then cause an increase in the period.
There are many examples of oscillating systems in addition to the three main ones normally addressed in introductory physics that were previously discussed. These may include circadian rhythms as well as the pulsating release of certain hormones, such as insulin, within the body. Identifying the factors affecting the period of these types of oscillators becomes much more difficult than simply looking at the equation to determine the relationship as there may be many outside factors affecting the period; however, a general understanding of the principle of the period of oscillation and its calculation for each of the examples may help to identify and research some the potential factors in more complex systems.