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- In the circuit below, assume that vs(t) = 12.5 cos(75000t) V is₁(t) = is₂(t) = 2 sin(75000t) A. Find the forced response for v(t). and 10 ΚΩ + vs(t) (1) isi(1) 1 nF = 10⁹ F v(t) Disz(1) Iarrow_forwardExercise 2. Consider the two continuous-time signals r(t) = u(t) – u(t - 2A) +00 y(t) = E Ar(t - k10A) %3! where 0 < A < +oo is a real constant. A) Derive the energy and the time-averaged power of both signals r(t) and y(t) over -00arrow_forward2. The circuit shown below is in DC steady-state before the switch flips at t = 0. ww 30 12 V 6Ω t = 0 -M 60 6H VL (t) ir(t) (a) Determine VL (0) and iL(0-). (b) For t > 0, determine the zero-state response, iL,zs(t), the zero-input response, iL,zı(t) and the full response, i(t). (c) For t> 0, determine VL(t). (d) Sketch vL (t) and i(t) for t> -1 clearly labelling important points.arrow_forwardThe systems given below have input x and output y. Determine whether each of them is memorlyless, stable, causal, linear and time invariant. y[n] = n x[n] %3D y(t) = x(2t) y(t) = (t + 1)x(t) y[n] = 2x[n]u[n] y(r) = x(sin(r)). %3Darrow_forwardThe circuit shown in Fig.15 is at steady state when the switch closes at time t=0. Determine i(t) for t2 0. 2 A 1 = 0 i (1) 5Ω 2 H 20 V 20 N 18 2 Fig.15arrow_forwardExample 1: Find the energy and power of the following continuos-time signals Determine whether each signal is an energy signal, power signal, or neither. a. x(t) = a, where a is a real-valued constant. b. x(t) = a, 0≤ t ≤ 1. c. x(t) = 10 sin(wot + 0) d. x(t) = 5e/tarrow_forwardObtain c(2) and c(3) and c(4) under the unit step input. (T 0.5) R(z) C(z) 1.2s ZOH § +1 T0.5arrow_forwardis(t) = A₁ cos s (1000 + 77) + A₂ ⋅ cos ( s (2000t - 7/7) Assume the system is in steady state. Find the current ia at times t₁ = 4πms: iα(t₁) = B₁ t25π ms: ia(t₂) = B₂ is(t) Given Variables: A1:2A A2:1A L: 2 mH C: 500 uF R1:2 ohm R2: 2 ohm K: 5 V/A Determine the following: B1 (A): B2 (A): www kia(t) R₁ |ia(t) C -R₂ ✗arrow_forward3. Determine the response y(n) for the following difference equation 3 y(n) –y(n – 1) +y(n – 2) = x(n) –x(n – 1) 4arrow_forwarddi(0+) Find in the following circuit: dt R1 L V,µ(-t) V( C R2 I,u(t) A If it is known that V, = 18 V, I, = 2 A, R1 = 6 N, R, = 2 N, C = 0.23 F y L = 0.31 H. %3Darrow_forward(1) For the system shown below do the following: R Determine the range of K for the system to be stable Determine the steady state error for a unit step input and a unit ramp input + K s(s+1)(s+2) Carrow_forwardConsider the system below. For this question, let C (s) = K, in this question K is a positive real number. a) Prove that if the root locus of the system is drawn, the points s1,2=−0.3214 ± 2.8951j will be on the curve. (Show it by doing mathematical calculation without drawing the curve.) b) Draw the root locus of the system. c) It is desired that the dominant (= near the imaginary axis) poles of the closed loop system be at the points s1,2= −0.3214 ± 2.8951j. What should K be for this? What can be said about the stability of the closed loop system for this K value? d) What are the unit step, ramp and parabolic reference tracking errors of the system for K in the option c?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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