What is the period of #f(t)=sin( t / 7 )+ cos( (t)/21 ) #?

2 Answers
Leland Adriano Alejandro
Jan 23, 2016

Period#=42pi#

Explanation:

#p_1=(2pi)/(1/7)=14pi#

#p_2=(2pi)/(1/21)=42pi#

the period for the sum is the # lcm(14pi, 42pi)=42pi#

Ken Rubenstein
Jan 23, 2016

nice Leland!...it's the same as a polyrhythm in music....LCMs are SO important!! If one musician is playing in one meter and a second musician is playing in another meter, you can manipulate all manner of LCMs for the sake of polyrhythms.

Here is a pretty TI screenshot to support the results.

enter image source here

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