Obtain the Fourier expansion of the function f(t) = t(T- t) in the interval 0 st...

 

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Obtain the Fourier expansion of the function f(t) = t(T- t) in the interval 0 st<T where T is the period. Hint: Here time is involved so let the Fourier series is ao f(t) 2 cos not + b, sin not n=1 n=1 Where w = Hint: Find ag, an and b, from their definitions like a, f(t)dt, an %3D 2 T So f(t) cos nwt dt and b, = f(t) sin nwt dt where f (t) = t(T -t) = Tt - t2 T2 T2 [cos wt T2 Answer: f(t): cos nat cos 2wt cos 3ait %3D ... 2 4n=1 12 22 32 Obtain the Fourier expansion of the function f(t) = t(T- t) in the interval 0 st<T where T is the period. Hint: Here time is involved so let the Fourier series is ao f(t) 2 cos not + b, sin not n=1 n=1 Where w = Hint: Find ag, an and b, from their definitions like a, f(t)dt, an %3D 2 T So f(t) cos nwt dt and b, = f(t) sin nwt dt where f (t) = t(T -t) = Tt - t2 T2 T2 [cos wt T2 Answer: f(t): cos nat cos 2wt cos 3ait %3D ... 2 4n=1 12 22 32