# Periodic motion – time period, frequency, displacement as a function of time

The periodic motion is the most common in the clock’s hands, in the wheels of the car, and the motion of the earth around the sun. All of these motions are repetitive as after the equal intervals of the time, the motion is being repeated. The motion that is repeating itself in the intervals of the time is the periodic motion. The circular motions are also periodic. As the equilibrium position of the body is in the path with itself.

### The formula of Period Motion

The motion of different bodies can be classified based on the way of their movement. For example, if a car is moving on the straight road, then it is said to be in the linear motion. The movement of the earth around the sun is a circular one. These movements are all termed as the periodic motions. The periodic motion can be expressed in terms of formula as f= I/T.

### Period and Frequency of the Period Motion

The period or interval of the time, in which the motion repeats itself after the equal intervals of the time is known as the periodic motion and it has the SI unit that is seconds. In each case for the interval of the time for every cycle of repetition, the motion is termed as period whereas, the number of periods per unit of the time is known as the frequency. So, the period of the orbiting of the earth is one year and the frequency of the earth orbiting is one orbit in 1 year. The tuning fork can have the frequency of the thousand cycles per second and the period of one millisecond that is one-thousandth part of the second.

### Displacement as a Function of Time

The displacement is the vector quantity and its length is the shortest distance ranging from the initial to the final position. It gives the quantification of both direction and distance of the imaginary motion along with a straight line from an initial position to the final position. The displacement can be described as the relative position. While considering the motions of the objects over time, the instantaneous velocity of the object is changed that is rate change of displacement, as a function of the time. This instantaneous speed is much distinct from the velocity or from the time rate of change in the distance traveled along the specific path.