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Plz explain Periodic Functions and also Rules for finding the period of the periodic functions ......

 Plz explain Periodic Functions and also Rules for finding the period of the periodic functions......

11 years ago

Answers : (1)

Vijay Luxmi Askiitiansexpert
357 Points
							

Periodic function

 

These are the function, whose value repeats after a fixed constant interval called period, and which makes a class of a widely used function.

        A function f of x, such that:

        f(T + x) = f(x) ∀ x ε domain of f.

        The least positive real value of T for, which above relation is true, is called the fundamental period or just the period of the function.

        e.g. for f(x) = sin x ∀ x ε R.

We know that sin (2∏ + x) = sin x, ∀ x ε R

so f(x) = sin x is a periodic function with a period of 2∏ radians.

 

  Rules for finding the period of the periodic functions

(i)     If f(x) is periodic with period p, then a f(x) + b, where a, b ε R (a≠0) is also a periodic function with period p.

(ii)    If f(x) is periodic with period, then f(ax + b), where a ε R -{0} and b ε R, is also periodic with period p/|a|.

(iii)    let us suppose that f(x) is periodic with period p and g(x) is periodic with period q. Let r be the L.C.M. of p and q, if it exists.

(a)    If f(x) and g(x) cannot be interchanged by adding a least positive number k, then r is the period of f(x) + g(x).

(b)    If f(x) and g(x) can be interchanged by adding a least positive number k and if k < r, then k is the period of f(x) + g(x). Otherwise r is the period.

 
11 years ago
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