Determine which of the following sinusoids are periodic and computetheir fundame

Question

Determine which of the following sinusoids are periodic and computetheir fundamental period.

(a) cos 0.01n

(b) cos((30n/105))

(c) cos 3n

(d) sin 3n

(e) sin((62n/10))

Explanation / Answer

Determine which of the following sinusoids are periodic and computetheir fundamental period. First of all recall the property of sinusoids that cos(ax) orsin(ax) are periodic with period is 2/|a| (a) Applying above property we get period of cos 0.01n=2/0.01 =200 (b) Period of cos((30n/105)) = 2/(3/105) = 70 (c) Period of cos 3n = 2/3 = 2/3 (if wewant period as integer, period = 2 ) If n is considered as integer. i.e. the domain of function isintegers by n+ period must also be integer => period must beinteger. (d) Period of sin 3n = 2/3 [ if we are looking for period tobe rational or integer then there is no value exsists for thisfunction. i.e. if n is an integer sin(3n) is notperiodic] (e) period of sin((62n/10)) =2/(62/10)=10/31 [ The least Integer period =10] ..........................................................

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