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Mechanical Properties Of Fluids

Question
CBSEENPH11019077

Show that y(t) = A sin ωt is periodic function of period 2 ϕ / ω.

Solution
Given,
y(t) = A sin ωt
We have to prove that y(t) is a  periodic function of period 2 ϕ / ω.
Therefore, 
straight y left parenthesis straight t right parenthesis space equals space straight y left parenthesis straight t plus fraction numerator 2 straight pi over denominator straight omega end fraction right parenthesis
Now comma

space space straight y left parenthesis straight t plus fraction numerator 2 straight pi over denominator straight omega end fraction right parenthesis equals straight A space sinω left parenthesis straight t plus fraction numerator 2 straight pi over denominator straight omega end fraction right parenthesis
space space space space space space space space space space space space space space space space space space space space equals space straight A space sin space left parenthesis ωt plus 2 straight pi right parenthesis

space space space space space space space space space space space space space space space space space space space space equals space straight A space sin space ωt

space space space space space space space space space space space space space space space space space space space space equals space straight y left parenthesis straight t right parenthesis
Therefore, y(t) is periodic function of period 2π /ω.