Question

Question 3 Please: Problem 1 is referenced below

3. Repeat problem 1 if the output y(t) is the voltage across the resistor instead of across the capacitor and the input is as shown in Figure 3 (you can use MATLAB to find the inverse Fourier Transform). [7 points] x(1) 0.5 Figure 3 1. For the circuit shown in Figure 1, find y(t) if the input is x(t) = 5 + 7 cos(10 t) + 7sin(1000t) co y()= vc) X(t)= v( Figure 1

Answer 1

From the given data, the voltge across the resistor in the following approach.
Given X(t):5. Feas(106) + 7 8in (1000) olp ytt) Voitaze a co the Teri01 In order to find the voltage arross the bov, The input anal hat different frequency. Co use the Super Polition theorem HR Voltage across the Rector NR:46): RA V 1 ) SCR 214) WRC Yt): VR Its CR THJW RC we know that 214): 5+10os (10) 44 Sn (1000 t). Split into different parts of lp afplied 1. Take the rlp aq 5 [freq:00 Yolt): VR.: 50.0 (becack the capacitor block the Ds Volu 2. Take the leat flos (tot) frez, ws to ] have. I cos (lot) (j to RC) *(1+j10RC) IVRel7 Cas (10+) (10RC) 51400RC)

3. Take the tip of the Sin (1000) (regco. 1000] 4s (t): VR.: 1 fin (100) (01000R) (1+j1000RC) 19. kl: 1 in (root) troop 1+(1000Rc)2 ytt): 9,1t) Y> [t) 4 Yolt) 10+ cos (10) CoR) Tin (1000t) (1000R) - SHIORCY Jit (1000R cje Cos (10) CIOR) 1 tin (1000 t) (OR) 11+(10R.)? rit (1000Rc)? Vo A class the Pero Alternate method Noltage Across the Resistor [VR IR here content Is le flowing through the [VR: IcR] Find le : c d rect to substitute (2) in (1) Ind 10 V (+) C'/se). V -2) wenget ic content flow Rulls (145CR) - through the Circolt throom Derio) uw we can find Voltage from the above Value Ic, Vc tt), weco across the the Residor [VR: ICR]