EXAMPLE 5
Find the period of f (t) =
Solution : If f (t) is periodic with period T then,
where m and n are integers.
Therefore T = 6mp = 8np
When m = 4 and n = 3, we get smallest value of T (by trial and error method)
Hence T = 24p
In general, if the function
f (t) = cos w_{1}t + cos w_{2}t is periodic with
period T then w_{1}T = 2mp and w_{2}T = 2np Þ
i.e. w_{1} / w_{2} must be a rational number.
EXAMPLE 6
Is the function f (t) = cos 10 t + cos (10 +
p )t periodic ?
Solution :
Therefore we cannot find T. Hence f(t) is not periodic.
EXAMPLE 7
Find the period of the function f(t) = (5 cos t)^{2}
Solution :
We know that cos^{2}x = 1/2 (1  cos2x)
We have f(t) = (5 cos t)^{2} = 25 cos^{2}t
Since if f (t) = K, constant function then
f (t+ T) = K = f (t) \ f (t) is periodic for any T
and cos 2t is periodic with period p.
