Simple Periodic Motion 

Frequency and Period

Frequency: 
       Frequency refers to how many waves are made per time interval. This is usually described as how many waves are made per second, or as cycles per second.

   Hertz is a unit of frequency (of change in state or cycle in a sound wave, alternating current, or other cyclical waveform) of one cycle per second. It replaces the earlier term of "cycle per second (cps)." Even though a Hertz is a per second, which would seem to me to be a base unit (because a second is a base unit).  It's not considered a base unit because a hertz is CYCLE / SECONDS which means in order to "measure" a hertz you would need to count (measure) the number of cycles and and time,  and thats why it's not a base unit

 Example:  Three waves are plotted for one second in the diagram above, each wave has a different frequency.  

The upper most plot shows a wave with a frequency of 20 Hz, It completes 20 full cycles in one second, 20 cycles / 1 sec = 20 Hz 

The middle plot shows a wave with a frequency of 40 Hz, it completes 40 full cycles in one second, 40 cycles / 1 sec = 40 Hz 

The bottom plot shows a wave of 80 Hz.  

Period:   

     Period refers to the time which it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. 

The Frequency Period Connection. Frequency is offend refereed to as the number of events that happens in a given time. Frequency simplified is simple cycles / Sec.  Period on the other hand is the amount of time it takes for a single event.  Period simplified is sec / cycle. 

  So the relationship between them is Frequency = 1 / Period 

  Example:

Three waves are plotted for one second in the diagram above, each wave has a different frequency.  

The upper most plot shows a wave with a frequency of 20 Hz, It completes 20 full cycles in one second, 20 cycles / 1 sec = 20 Hz. The period is 1/20 sec, It takes 1/20 th of a second for that event to happen again

The middle plot shows a wave with a frequency of 40 Hz, it completes 40 full cycles in one second, 40 cycles / 1 sec = 40 Hz.  The period is 1/40 sec, it takes only 1/40 th of a second for that event to happen again 

The bottom plot shows a wave of 80 Hz. The period is 1/80 sec.

Angular Frequency

  Angular frequency ω (also referred to by the terms angular speed, radial frequency, and radian frequency) is a scalar measure of rotation rate.

Angular frequency is the magnitude of the vector quantity angular velocity. The term angular frequency vector  is sometimes used as a synonym for the vector quantity angular velocity .

In SI units, angular frequency is measured in radians per second, with dimensions of Per second since radians are dimensionless.

Pendulum

       A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by the equation above. 

Equations provided by HyperPhysics

Springs

       The frequency of simple harmonic motion like a mass on a spring is determined by the mass m and the stiffness of the spring expressed in terms of a spring constant k (see Hooke's Law)

Equation provided by HyperPhysics

T = Period

m = Mass of the bob

L = Length from point of pivot to center of the bob

k = Spring constant

g = acceleration due to gravity