. A continuous-time system is given by the input/output differential equationd²y(t)dt²dy(t)+4- + 3y(t) = 2d²x(t)-4-dtdt²dx(t)dt-x(t):=unit impulseIn each of the following parts, compute the response y(t) for all t ≥ 0.(a) y(0) = −2, y(0¯) = 1, x(t) = 0 for all t≥0.(b) y(0) = 0, y(0¯) = 0, x(t) = d(t), 8(t)(c) y(0) = 0, y(0¯) = 0, x(t) = u(t)(d) y(0¯) = −2, y(0¯) = 1, x(t) = u(t)

Step 1:Solving the given differential equation for different initial conditions and input signals…

Answered: . A continuous-time system is given by…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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A system is described by the following differential equation dx +4 +2x%31 dt dt with the initial conditions x(0) = 2, = -2. Show a block diagram of the system and all pertinent inputs and outputs.
What is the steady-state error to a unit-step input R(s) == for the system below? R(s) + 6 C(s) s+3 Select one: O a. ess = lim (r(t)- c(t)) 1-x 2 O b. e.. = lim (r(t) - c(t)) = 0 1-x 1 OC. Ess = lim (r(t)- c(t)) = 3 t-00 O d. ess = lim (r(t)- c(t)) = ∞ 14x
a) Read the following signal f(t), (write out the equation using a combination of unit-step and ramp functions) b) Draw f(t+1)
1) For the continuous-time signal x(t) indicated in Figure 1, sketch and label the following signals, also verify your results using MATLAB. (a) x(-t) (b) x(t + 2) (c) x(2t + 2) (d) x(1 – 3t) x(t) 1
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Find the steady-state oscillations of y" + cy' + y = r(t) with c > 0 and r(t) as given. Note that the spring constant is k = 1. Show the details. In Probs. 14–16 sketch r(t). 16. r(t) = t if -1/2
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Compute the convolution between signal F(t) and G(t) by shifting F(t), i.e., use the following equation to compute your convolution F(t) * G(t) = | F(t – t)G(t) dr - 00 F(T) = U(T-155)-U(t+155) G() 100+ 50 -100 100 Recommended steps to follow while solving 1. Draw the signal F(t) by properly labelling the axis 2. Draw the signal G(t) by properly labelling the axis 3. Draw the signal F(t – t) by properly labelling the axis and mentioning the condition of t 4. Draw the signal G(t) by properly labelling the axis 5. Compute the convolution now by properly defining ranges of t for which two signals do not overlap, partially overlap or full overlap.
Sketch the following continuous time signals. 1. x(t) = u(t-1) + u(t - 2) 2. x(t) = 2u(3t - 9) 3. x(t) = (4t+2)(u(t-2) - u(t - 5)) 4. x(t) = 2e¹(u(t - 2) - u(t - 4))

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