What is the period of #f(t)=sin( 4 t )+ cos( (7t)/24 ) #?

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Answer 1 · 2016-07-17T03:39:37

#48pi#

The period for sin kt and cos kt = #(2 pi)/k.

Here, the separate periods for #sin 4t and cos ((7t)/24)# are

#P_1=(1/2)pi and P_2=(7/12)pi#

For the compounded oscillation

#f.(t)=sin 4t + cos((7t)/24)#,

If t is increased by the least possible period P ,

f(t+P) =f(t).

Here, ( the least possible ) P= 48 pi= (2 X 48)P_1=((12/7) X 48) P2#.

#f(t+48 pi) = sin (4(t+48 pi ))+cos((7/24)(t+48 pi))#

#=sin (4 t+192 pi)+cos((7/24)t+14 pi)#

#=sin 4 t + cos (7/12)t#

#=f(t)#

Note that #14 pi# is the least possible multiple of (2pi)#.