Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system.
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5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1...
Consider the following circuits connected in series. The input is the voltage x(t), the output to...
Consider the following circuits connected in series. The input is the voltage x(t), the output to system Si is the voltage y(t), and the output of system S2 is the voltage y(t). The differential equation relating the input X(t) to the output yı(t) was found in Homework #3. S2 x(1) y(t) | X(t) 6+ R yce) .66) (1) + y(t) Let L = 0.01, C1 = 0.01, R = 100, C2 = 0.002, and R2 = 50. a) Find the...
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse...
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse response of the system. (b) Find the zero-state response when the input is a unit step. (c) Find the zero-state response when the input is x(t) = 1.6u(t) − 0.6u(t − 1).
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) +...
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
An LTI system, with an input g(t) and an output y(t), is represented with the following...
An LTI system, with an input g(t) and an output y(t), is represented with the following state and output matrices. Assuming a zero-state condition, identify the steady state error if the system is subject to a unit step function. [x1 [x2. ) = [] : [22] + [3] AND y = [2 -1) [x3] + [2]g 4. 0 2 1 3 5
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t)...
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
1. For a system described in Figure 1. x(t) - input voltage, y(t) - output voltage....
1. For a system described in Figure 1. x(t) - input voltage, y(t) - output voltage. (a) Determine Continuous Time (C.T.) "Math Model" when R = 1/3 121, L = 1/2 [F], and C = 1 [F]. (b) Fine "Zero Input Response". y zit. for the C.T.system. when y(0) = 1 [V], y'(0) = 2 IV (c) Draw "Zero Input Response". y_zi(t) with respect to time 1 (2-D graph) (d) Find impulse response, h(!). of the Continuous Time (C.T.) system....
4- Find unit impulse response for: y(t) + 4у(t) + 3y(t)-x(t) + 5x(t) 5- Find the...
4- Find unit impulse response for: y(t) + 4у(t) + 3y(t)-x(t) + 5x(t) 5- Find the total response for: ý(t) 13(t) 22y(t)-(t) +5x(t) x(t) e-Stu(t) With the initial condition y(0) 2 and y(0)-3 Identify the natural and forced response of the system. 6- Find the total response for: y(t) +2y(t) 17y(t) 4x(t) 8x(t) x(t) = e-Hu(t)
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are related by Y(s) = 2 (s+2)2 +10 a) If x(t) = u(t), find the zero-state response of the system, yzs(1). yzs() = b) Find the zero-input response of the system, yzi(t). Yzi(t) = c) Find the steady-state solution of the system, yss(t). Yss(t) =
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady...
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady State response: Unit Impulse response and Convolution Integral (Zero-State response): 9) Two LTI systems in parallel h1(t)- e "u(t) and h2(t)- h1(t-2) a. Find the expression of the combined unit impulse response h(t) b. Find the zero state response y2s(t) in the expression of piecewise function to the input signal x(t)-[u(t)-u(t-10)] Sketch y2s(t) Show that the combined system h(t) is causal as well as...
Consider the following circuits connected in series. The input is the voltage x(t), the output to system Si is the voltage y(t), and the output of system S2 is the voltage y(t). The differential equation relating the input X(t) to the output yı(t) was found in Homework #3. S2 x(1) y(t) | X(t) 6+ R yce) .66) (1) + y(t) Let L = 0.01, C1 = 0.01, R = 100, C2 = 0.002, and R2 = 50. a) Find the...
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
An LTI system, with an input g(t) and an output y(t), is represented with the following state and output matrices. Assuming a zero-state condition, identify the steady state error if the system is subject to a unit step function. [x1 [x2. ) = [] : [22] + [3] AND y = [2 -1) [x3] + [2]g 4. 0 2 1 3 5
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
1. For a system described in Figure 1. x(t) - input voltage, y(t) - output voltage. (a) Determine Continuous Time (C.T.) "Math Model" when R = 1/3 121, L = 1/2 [F], and C = 1 [F]. (b) Fine "Zero Input Response". y zit. for the C.T.system. when y(0) = 1 [V], y'(0) = 2 IV (c) Draw "Zero Input Response". y_zi(t) with respect to time 1 (2-D graph) (d) Find impulse response, h(!). of the Continuous Time (C.T.) system....
4- Find unit impulse response for: y(t) + 4у(t) + 3y(t)-x(t) + 5x(t) 5- Find the total response for: ý(t) 13(t) 22y(t)-(t) +5x(t) x(t) e-Stu(t) With the initial condition y(0) 2 and y(0)-3 Identify the natural and forced response of the system. 6- Find the total response for: y(t) +2y(t) 17y(t) 4x(t) 8x(t) x(t) = e-Hu(t)
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are related by Y(s) = 2 (s+2)2 +10 a) If x(t) = u(t), find the zero-state response of the system, yzs(1). yzs() = b) Find the zero-input response of the system, yzi(t). Yzi(t) = c) Find the steady-state solution of the system, yss(t). Yss(t) =
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady State response: Unit Impulse response and Convolution Integral (Zero-State response): 9) Two LTI systems in parallel h1(t)- e "u(t) and h2(t)- h1(t-2) a. Find the expression of the combined unit impulse response h(t) b. Find the zero state response y2s(t) in the expression of piecewise function to the input signal x(t)-[u(t)-u(t-10)] Sketch y2s(t) Show that the combined system h(t) is causal as well as...
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