Identify the periodic functions and their time periods, if any from the following (i) sin 2t , (ii) sin 3t , (iii) sint + cos t , (iv) sin t + sin 3t (v) e^(-1)

Identify the periodic functions and their time periods, if any from th

1.	Identify the periodic functions and their time periods, if any from the following (i) sin 2t , (ii) sin 3t , (iii) sint + cos t , (iv) sin t + sin 3t (v) e^(-1)
Answer» SOLUTION :If can be written as `sin 2T = sin (2t + 2pi) = sin 2(t+ pi)` Comparing with equation 5.1, time period of given function is `pi` units. (ii) `sin 3t = sin (3t + 2pi) sin 3 (t+ (2pi)/(3)) therefore ` Time period , `T= (2pi)/(3)` (iii) After trigonometric transformations, the given functions can be written as `sin t + COS t = sqrt2 sin [omega t + pi/4]` , Since it is a sine function , its time period is also `2pi` Note that the linear combination of time and COSINE functions , such as `f(t) = A sint + B cost ` is also periodic of time period `2pi` (IV) The time period of sin t and sin 3t are `2pi and 2pi//3` as already discussed in above examples . Since the given function can repeat it self only after a time of `2pi` , its time period is `2pi` . (v)The plot of `e^(-1)` vs t is an shown From the graph , it is easy to say that the given function is not periodic .