Periodic Function Equation Math

A periodic function is a function that repeats its values at regular intervals for example the trigonometric functions which repeat at intervals of 2π radians periodic functions are used throughout science to describe oscillations waves and other phenomena that exhibit periodicity any function that is not periodic is called aperiodic.

Periodic function equation math. A b is a periodic function if it satisfies the rule ƒ x t ƒ x for all values of x in a. In mathematical terms we say that a periodic function is a function for which a specific. What are periodic functions. For the following exercises graph one full period of each function starting at x 0.

State the maximum and minimum y values and their corresponding x values on one period for x 0. In the problems below we will use the formula for the period p of trigonometric functions of the form y a sin bx c d or y a cos bx c d and which is given by. The midline often represents the average value of a wave like periodic function and should always be written as the equation of a horizontal line this means that. To obtain the graph of f it is sufficient to have the graph of f on a a t cap x where a is a certain number and shift it along mathbf r over pm t pm 2t dots.

A function with this property is called a periodic function. Periodic functions are applied to study signals and waves in electrical and electronic systems vibrations in mechanical and civil engineering systems waves in physics and wireless systems and has many other applications. A periodic function is a function whose output values repeat on a regular interval. Find period of trigonometric functions.

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Illustrated definition of periodic function. The values of some mathematical functions repeat with the same pattern to infinity. Grade 12 trigonometry problems and questions on how to find the period of trigonometric functions given its graph or formula are presented along with detailed solutions.

Period of a function. The number t is called the period of the function. Graphs of the other trigonometric functions for the exercises 1 4 graph the functions for two periods and determine the amplitude or stretching factor period midline equation and asymptotes. If the periodic function can be represented by a sine curve then the motion is said to be simple harmonic motion like a weight on spring oscillating a swing etc.

State the phase shift and vertical translation if applicable. Let a function f be defined on x subset mathbf r and have period t. A function like sine and cosine that repeats forever.