What is the period of #f(t)=sin( (t)/4 )+ cos( (t)/12 ) #?

1 Answer
Apr 17, 2016

#24pi#

Explanation:

The period of both sin kt and cos kt is #(2pi)/k#.
For the separate oscillations given by #sin(t/4) and cos(t/12)#, the periods are #8pi and 24pi#, respectively.

So. for the compounded oscillation given by #sin(t/4)+cos(t/12)#, the period is the LCM = #24pi#.

In general, if the separate periods are #P_1 and P_2#, the period for the compounded oscillation is from #mP_1=nP_2#, for the least positive-integer pair [m, n].

Here, #P_1=8pi and P_2=24pi#. So, m = 3 and n = 1.