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1 For the circuit below, use the Laplace transform to a. Find the total response, y(t),...
Consider the differential equation: 0)+ y(t)-x(), and use the unilateral Laplace Transform to solve the following...
Consider the differential equation: 0)+ y(t)-x(), and use the unilateral Laplace Transform to solve the following problem. a. Determine the zero-state response of this system when the input current is x(t) = e-Hu(t). b. Determine the zero-input response of the system for t > 0-, given C. Determine the output of the circuit when the input current is x(t)- e-2tu(t) and the initial condition is the same as the one specified in part (b).
1. Find the Laplace transforms of these functions: r(t) = tu(t), that is, the ramp function;...
1. Find the Laplace transforms of these functions: r(t) = tu(t), that is, the ramp function; Ae-atu(t); Be atu(t). 2. Determine the Laplace transform of f(t) = 50cos ot u(t). 3. Obtain the Laplace transform of f(t) = (cos (2t) + e 41) u(t). 4. Find the Laplace transform of u(t-2). 5. Find vo(t) in the circuit shown below, assuming zero initial conditions. IH F + 10u(i) 42 v. (1)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse...
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the...
Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the output is eo. 1). Find the state variable model. Take ec and IL as state variables (refer notes from Chapter-6). 2). Apply Laplace Transform on the state variable model (from part-1) and show that the transform of the output (eo) is given by the expression: 사스 ; if the initial conditions, L(0) and ec(0) are known. Note: ec(0)-eo(0) R L R L...
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) =
The Laplace transform of y(t) is Y(s). Find the Laplace transform of po py(e) + 8...
The Laplace transform of y(t) is Y(s). Find the Laplace transform of po py(e) + 8 minute) –80(), in terms of Y(s), using y(0) = 4 and y' (O) = 3. (Do not forget to use a multiplication sign when multiplying.) and are not to mentioning el seu pare sa ive) – 8,0}-
Q3. (1) Initial energy stored in the circuit is zero. Use Laplace transform to find Thevenin...
Q3. (1) Initial energy stored in the circuit is zero. Use Laplace transform to find Thevenin equivalent voltage (Vth) and Thevenin equivalent impedance (Zth) in the s domain with respect to terminals 'a' and 'b'. (12 points) 22 M 20u(t) (2) Find the time-domain solution for current iz(t). (8 points)
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...
Section 3: Laplace transform for RLC circuit analysis (10 marks) A second-order RLC circuit with a...
Section 3: Laplace transform for RLC circuit analysis (10 marks) A second-order RLC circuit with a dependent source is shown in Fig. 3. 22 + VO - 132 1F + 15e-2 u(t) V ) 9[1-u(t)] V Y 0.50 » Fig. 3 A second-order RLC circuit with a dependent source Take the Laplace transform of the circuit and hence find the response io(t) for t > 0. Specify whether it is an underdamped, critically damped or overdamped case. Sketch the response.
System Modeling and Laplace transform: In this problem we will review the modeling proce- dure for the RLC circuit as shown below, and how to find the corresponding transfer function and step respons...
System Modeling and Laplace transform: In this problem we will review the modeling proce- dure for the RLC circuit as shown below, and how to find the corresponding transfer function and step response Ri R2 Cv0) i2) i,(0) 3.1 Considering the input to be V(t) and the output to be Ve(t), find the transfer function of the system. To do that, first derive the differential equations for al the three loops and then take the Laplace transforms of them. 3.2...
Consider the differential equation: 0)+ y(t)-x(), and use the unilateral Laplace Transform to solve the following problem. a. Determine the zero-state response of this system when the input current is x(t) = e-Hu(t). b. Determine the zero-input response of the system for t > 0-, given C. Determine the output of the circuit when the input current is x(t)- e-2tu(t) and the initial condition is the same as the one specified in part (b).
1. Find the Laplace transforms of these functions: r(t) = tu(t), that is, the ramp function; Ae-atu(t); Be atu(t). 2. Determine the Laplace transform of f(t) = 50cos ot u(t). 3. Obtain the Laplace transform of f(t) = (cos (2t) + e 41) u(t). 4. Find the Laplace transform of u(t-2). 5. Find vo(t) in the circuit shown below, assuming zero initial conditions. IH F + 10u(i) 42 v. (1)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the output is eo. 1). Find the state variable model. Take ec and IL as state variables (refer notes from Chapter-6). 2). Apply Laplace Transform on the state variable model (from part-1) and show that the transform of the output (eo) is given by the expression: 사스 ; if the initial conditions, L(0) and ec(0) are known. Note: ec(0)-eo(0) R L R L...
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) =
The Laplace transform of y(t) is Y(s). Find the Laplace transform of po py(e) + 8 minute) –80(), in terms of Y(s), using y(0) = 4 and y' (O) = 3. (Do not forget to use a multiplication sign when multiplying.) and are not to mentioning el seu pare sa ive) – 8,0}-
Q3. (1) Initial energy stored in the circuit is zero. Use Laplace transform to find Thevenin equivalent voltage (Vth) and Thevenin equivalent impedance (Zth) in the s domain with respect to terminals 'a' and 'b'. (12 points) 22 M 20u(t) (2) Find the time-domain solution for current iz(t). (8 points)
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...
Section 3: Laplace transform for RLC circuit analysis (10 marks) A second-order RLC circuit with a dependent source is shown in Fig. 3. 22 + VO - 132 1F + 15e-2 u(t) V ) 9[1-u(t)] V Y 0.50 » Fig. 3 A second-order RLC circuit with a dependent source Take the Laplace transform of the circuit and hence find the response io(t) for t > 0. Specify whether it is an underdamped, critically damped or overdamped case. Sketch the response.
System Modeling and Laplace transform: In this problem we will review the modeling proce- dure for the RLC circuit as shown below, and how to find the corresponding transfer function and step response Ri R2 Cv0) i2) i,(0) 3.1 Considering the input to be V(t) and the output to be Ve(t), find the transfer function of the system. To do that, first derive the differential equations for al the three loops and then take the Laplace transforms of them. 3.2...
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