(Solved): Given the following periodic waveform with period T=6,f(t)={(20,-1<=t<=1),(0,1<=t<5):}. ...

Given the following periodic waveform with period

T=6,f(t)={(20,-1<=t<=1),(0,1<=t<5):}

. (a) Find the symmetry: Odd only Odd and half-wave Even and half wave No symmetry Half wave only Even only (b) Calculate

a_(0)

and

w_(0)

a_(0)=,;,\omega _(0)=

Express

a_(0)

to 3 significant digits and give the exact value for

\omega _(0)

. Type Pi for

\pi

. (c) Which of the following is the Fourier Series expansion for the given function? (zero harmonics are omitted).

b_(1)sin((1)/(3)\pi t)+b_(3)sin(\pi t)+b_(5)sin((5)/(3)\pi t)+a_(7)sin((7)/(3)\pi t) a_(1)cos((1)/(3)\pi t)+a_(3)cos(\pi t)+a_(5)cos((5)/(3)\pi t)+a_(7)cos((7)/(3)\pi t) a_(0)+a_(1)cos((1)/(3)\pi t)+a_(2)cos((2)/(3)\pi t)+a_(3)cos(\pi t)+a_(4)cos((4)/(3)\pi t) b_(1)sin((1)/(3)\pi t)+b_(2)sin((2)/(3)\pi t)+b_(3)sin(\pi t)+b_(4)sin((4)/(3)\pi t)

(d) Which of the coefficients

a_(n)

or

b_(n)

are zero? For non-zero coefficients, round to 3 significant digits.

a_(n)= b_(n)=

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