What is the period of #f(t)=sin( t / 14 )+ cos( (t)/21 ) #?

1 Answer
A. S. Adikesavan
Apr 19, 2016

#84pi#

Explanation:

The period for both sin kt and cos kt is #(2pi)/k#

The periods of the two separate oscillations in f(t) are #28pi and 42pi#.

The period for the compounded oscillation is such that 28 M = 42 N, for lowest positive integers M and N. Easily, M =3 and N = 2. These give the LCM common value #84 pi# as the period for f(t).
#f(t+84pi)=sin(t/14+6pi)+cos(t/21+4pi)= sin(t/14)+cos(t/21)=f(t)#

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