What is the period of #f(t)=sin( t /44 )+ cos( (7t)/24 ) #?

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Answer 1 · 2016-08-12T07:53:31

#528pi#

The period for both sin kt and cos kt i #2pi/k#.

Here, the periods for the separate oscillations #sin(t/44) and cos

(7t/24)# are #88pi and 48/7pi#, respectively.

The period P for the compounded oscillation f(t) is given by

#P = L(88pi)=M(48/7pi)#, where L and M are least positive integer

multiples to give P as the least even positive integer.

For .#L = 6 and M = 77, least P = 528pi#.

See how it works.

#f(t+P)#

#=f(t + 528pi)#

#=sin(t/44+24pi)+cos(7/24t+154pi)#

#=sin(t/44)+cos(7/24t)#

#=f(t).

Note the if P is halved , the second term would become its negative.