What is the period of #f(t)=sin( t / 18 )+ cos( (t)/ 48 ) #?

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Answer 1 · 2016-05-10T15:54:13

#576pi#

For both sin kt and cos kt, the period is #(2pi)/k#.

So, the separate periods of oscillations for #sin t/18 and cos t/48 are

#36pi and 96pi#.

Now, the period for the compounded oscillation by the sum is

LCM# = 576pi# of #36pi and 96pi#.

Jusr see how it works.

#f(t+576pi)#

#=sin (1/18(t+576pi)) + cos (1/48(t+576pi))#

#=sin(t/18+32pi)+cos(t/48+12pi)#

#=sin (t/18)+cost/48#

#=f(t)#..