Formula for Time Period

Time period is the recorded amount of time that is required for a physical or chemical change. The time period is different for different variable systems in the universe. For example, when a pot of water is being boiled, the time period for the water to come to a boil is different from the time period for the water to cool down. The water coming to a boil requires the water to increase in temperature, which is a physical change.

Time period, also known as time interval, is the duration of time that was taken for a physical or chemical change. The time period is different for different variable systems in the universe. For example, a pendulum clock has a specific formula of time period, which means that it will take the same amount of time for the pendulum to swing back and forth. If the pendulum is moved to a different place, the pendulum will swing back and forth at the same speed, but the variations in the formula of time period will be different because the pendulum is now in a different place.

The formula for time period

The basic formula of time period can be expressed as follows: T Period = Tinitial – Tfinal, where Tperiod is the time period, Tinitial is the initial time, and Tfinal is the final time. The time period can be used to determine the amount of time that has passed since the beginning of the physical or chemical process. The formula of time period can be used to determine the amount of time that has passed in different situations in physics. The formula of time period can also precisely be utilised to to calculate the speed of a system, with given the distance coordinates in the unidirectional motion.

The formula of time period in different physical systems

The time period of a system is a function of measurement of duration of a change, and this is commonly symbolised by the capital letter T in physics. The time period is determined in the proper time units for a specific system, however, seconds are the most commonly used metric of determining the time period in physics. The second is a measure of time that was actually based on the earth’s rotation on its axis and also its revolution around the sun, but the present interpretation is based on the oscillations of the cesium-133 positive atom rather than any astrophysical occurrence. 

Formula of time period in one dimensional motion

Suppose a system goes from point A to point B, and the distance between the points A and B is x , the given speed of the system is v. The formula of time period of its motion from point A to point B is given by –

                                   T(time period) = x (Distance)/ v (speed)

Formula of time period in projectile motion

Let us consider a projectile launched with speed u at an angle 𝛳 to the horizontal. The horizontal component of the velocity is given by ucos𝛳 and the vertical component of the velocity of the projectile is given by usin𝛳. It is to be noted that the vertical component of the velocity becomes zero at the highest point of the projectile. By applying one directional motion equations to the both x and y axis components of the projectile gives the formula of time period as-

                                          T = 2usin𝛳/g 

Relation between time period and frequency 

The time period of a system in periodic motion is the time it takes to complete a single complete motion, whereas the frequency ( f ) is the number of complete  motions the system can accomplish in a specified time period. Our  Planet, for example, revolves once per day, therefore the  time duration is one day, and indeed the frequency is one cycle per day. When the time system is established to years, the time period is 1/365 years, and the frequency is 365 cycles each year. The variable values of time period and frequency are related in a reciprocal manner. 

Formula of time period in oscillatory systems

The formula of the simple pendulum time period is co- dependent on the frequency of the oscillations of the pendulum. A simple pendulum is one of the most basic sorts of periodic motion, described as one which constantly builds up an acceleratory impulse proportional to its distance from mean position and is oriented toward the equilibrium point. A pendulum and a mass coupled to spring can both be simple harmonic oscillators, provided that there is a lack of friction force. 

Pendulums are widely used. Some are critical, such as in wall-clocks.  A pendulum is a basic harmonic oscillator for tiny displacements. A simple pendulum is an item with a little mass, frequently referred to as the pendulum bob, hanging from a thin lightweight wire or thread. Let us consider a pendulum of length l and is suspended with an angle 𝛳 from the mean position. The acceleration gravity acts upon the pendulum bob of mass m and hence tension is observed in the string of the pendulum. The formula of simple pendulum time period is given by- 

                                                      T = 2𝝅√L/g

Conclusion

Time period, the noted duration of time that was utilised for a physical or chemical change in either of the processes. The metrics of time period are different for different variable systems in the universe. The formula of time period can be used to determine the change, record the periodic processes such as radioactive decay, atomic clocks, etc. Time period in oscillatory motion, like that of a simple pendulum, is the amount of time used to cover the displacement from the mean to extreme and back to the mean position.