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Periodic Motion

Period motion is repeated motion at equal intervals of time. There are many different examples of periodic motion being performed, a bounding call, vibrating tuning fork, a rocking chair or a water wave. The interval for a single repetition or cycle is called a period. The number of periods per unit of time is called its frequency. For example, a period of the Earth’s orbit is one year and its frequency is one orbit per year.

Period= 1/frequency

Frequency= 1/period

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. The phenomena of simple harmonic motion can be seen in the motion of a simple pendulum and molecular vibration. The equation of the restoring force, F, can be seen in the following equation:

F= -kx

Where k is the spring constant and x is the displacement from the equilibrium.
The sinusoidal function of a simple harmonic motion can be solved using a differential equation

x(t)= c_1 cos(ωt)+ c_2 sin(ωt)=Acos(ωt- φ)

Where

ω= √(k/m)

A= √(c_1^2+c_2^2 )

tan〖φ= c_2/c_1 〗

Where c_1 and c_2 are constants that can be solved for.

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