Sat March 24, 2012 By:

Why do we add T to f(t) such that f(t + T) to express a periodic function..? Explain

Expert Reply
Sat March 24, 2012
Periodic function is a function which repeats itself in regular time scale.Periodic functions are functions which repeat:  f(t + P) = f(t) for all t. For example, if  f(t) is the amount of time between sunrise and sunset at a certain lattitude, as a function of time t, and P is the length of the year, then f(t + P) = f(t) for all t, since the Earth and Sun are in the same position after one full revolution of the Earth around the Sun. We  state this  explicitly  as the following de?ntion:  a function  f(t) is periodic with period P > 0 if f(t + P) = f(t) for all t. Example. f(t) = sin(2t) is periodic with period P = ?. This is true because, for all t, f(t + ?) = sin(2(t + ?) = sin(2t + 2?) = sin(2t) = f(t). Notice, though, that in the example above  f(t) = sin(2t) also has period P = 2? and period P = 3?.  In fact, it has period P = n? for any integer n = 1, 2, 3 . . . . Graphically, a function with period P is one whose graph stays the same if it is shifted P to the left or right.
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