Answer Happy

This problem is related to Problem 9.25-9.27 in the text.
The periodic function s0(t)s0(t) with
period 2020 given by
s0(t)=⎧⎩⎨⎪⎪010 if −10≤t<−0.5 if −0.5≤t<0.5 if 0.5≤t<10.s0(t)={0 if −10≤t<−0.51 if −0.5≤t<0.50 if 0.5≤t<10.
has the Fourier series defined by
S0(0)=0.05S0(0)=0.05
and for n≠0n≠0
S0(n)=0.05∗sin(nπ1/20)nπ1/20S0(n)=0.05∗sin⁡(nπ1/20)nπ1/20
Use linearity and the shifting property to find the Fourier
Series for s(t)s(t), defined by
s(t)=⎧⎩⎨⎪⎪⎪⎪⎪⎪0−3−20 if −10≤t<2 if 2≤t<3 if 3≤t<4 if 4≤t<10.s(t)={0 if −10≤t<2−3 if 2≤t<3−2 if 3≤t<40 if 4≤t<10.
S(0)=S(0)= ,
and for n≠0n≠0
S(n)=S(n)= .
(25 points) This problem is related to Problem 9.25-9.27 in the text. The periodic function so (t) with period 20 given by 0 So (t) = = 1 if – 10 <t< -0.5 if – 0.5 < t < 0.5 if 0.5 < t < 10. - 0 has the Fourier series defined by S.(0) = 0.05 and for n +0 So(n) = 0.05 * sin(na 1/20) na1/20 Use linearity and the shifting property to find the Fourier Series for s(t), defined by 0 - s(t) = دل ا ه if – 10 <t< 2 if 2 < t < 3 if 3 < t < 4 if 4 < t < 10. -2 = S(0) = and for n = 0 S(n) =