1. Consider the system below x(t) v(t) y(t) System-1 System-2 The input and output relationship of the two systems are v(t) = h₁(t) * x(t), where h₁ (t) = r(t) and y(t) = v(7) dr and the System-2 is linear. a) Show that System-2 is time invariant. b) Is the overall system linear and time invariant? Justify. c) Determine the impulse response of System-2. d) Determine the overall impulse response of the system.

1. Consider the system below x(t) v(t) y(t) System-1 System-2 The input and output relationship of the two systems are v(t) = h₁(t) * x(t), where h₁ (t) = r(t) and y(t) = v(7) dr and the System-2 is linear. a) Show that System-2 is time invariant. b) Is the overall system linear and time invariant? Justify. c) Determine the impulse response of System-2. d) Determine the overall impulse response of the system.

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...

See similar textbooks

Similar questions

The mathematical models of some continuous time systems are given above. x(t) is the input signal of the system, and y(t) is the output signal of the system. Which of the following systems is linear and which is nonlinear? For linear systems, write "linear" in the space next to the option. For non-linear systems, write "non-linear" in the space next to the option.
Consider two systems one is second order and the other is third order. The characteristic equations are: as2+bs+c for the second order and as3+bs2+cs+d for the third order, where a,b,c,d are positive real numbers. Then which of the following is correct with regard to the stability of these two systems? a. stability of either system cannot be confirmed with the given data b. third order is definitely stable but second order cannot be confirmed c. both systems are definitely stable d. second order is definitely stable but third order cannot be confirmed
a discreate time , linear time variant dynamic system is described by difference equation y[k+2]-y[k]=0.5u[k], k>=0, y[0]=1, y[1]= 0 a. rewrite the system dynamics in the controlable canonical form. b. is the system asymptomtic satble?
The following equation is linear, constant-coefficient, homogeneous ordinary differential equation. my′′(t) + Ks y(t) = mg + 30Ks Select one: True False
identify the following 1. If the pole’s real value is positive and is located on the right side of the S-plane. The system exponentially ____________.2. Is a continuous connection of branches from one node to another with all arrowheads in the same direction.3. Knowing the location of the pole in the S-plane determines the ______________ of the system.
. A continuous-time system is defined by an input-output relation as; y(t) = 3x(t) – 5x(t+1) Determine whether this system has the properties given below. i) Memoryless, ii) Causal, iii) Stable, iv) Linear, v) Time-invariant.
consider the translational mechanical network system a 1lb force f(t), si applied at t=0 if fv=1 find K and M such response is characterized by 4 sec settling time and 1 sec peak time also what is the resulting %OS
Inside a system contains two small discrete time systems X and Y. X: y[n] = ax[n] + bx[n-1] + cx[n-2] , where a, b, and c are real constants Y: y[n] = med{x[n-1], x[n], x[n+1]} , where med is taking median value of three inputs. Explain and prove why different order of the two systems yields two different results.
A) Reduce the block diagram. B) G1(s)= 2/s, G2(s)= 1/4s+2, G3(s)=4, H(s)=0.5 according to the given values, find the system's time constant, natural frequency, and damping rate, and explain what dynamic behavior it will exhibit accordingly. C) G1(s)= 2/s, G2(s)= 1/4s+2, G3(s)=4, H(s)=0.5 Find the poles and zeros of the system according to the given values. Accordingly, specify whether the system is stable. Find the unit digit response (reverse laplace)
G(s)=((s+1)*(s+15))/((s+0.1)*(s+2.5)*(s+120)*(s+240)) 1-draw nyquist 2- Nyquist criterion, compute the number of unstable poles of the closed loop system as a function of K 3-determine for which values of K the closed system is stable.
Obtain the value of I1, if M=1/√2H, and the circuit is in steady state at t = 0.
In particular, a system may or may not be(1) Memoryless(2) Time invariant(3) Linear(4) Causal(S) StableDetermine which of these properties hold and which do not hold for the following continuous-time system. Justify your answers.