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PROBLEM #2: In the circuit shown, suppose that R and C are given. The transfer function...
a. (10) For the circuit below, draw the s-domain equivalent circuit and show that H(S) =...
a. (10) For the circuit below, draw the s-domain equivalent circuit and show that H(S) = 2 2 . 2321H 0.5F V b. (10) Using Inverse Laplace Transforms, find the impulse response (1) c. (5) Briefly tell me in your own words what an impulse response is. d. (15) For an input, vt) = 2e- Transforms to find vo(t). use Laplace Transforms to find V.(s) and then use Inverse Laplace e. (5) Briefly discuss how convolution could have been used...
problem 7 Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure....
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
suppose an input voltage is given as V(t) = 240[u(t-5) - u(t-10)]. In a branch of an electronic circuit, the variation of current with time is modeled by the differential equation d^2(i)/dt^2 + 36i =...
suppose an input voltage is given as V(t) = 240[u(t-5) - u(t-10)]. In a branch of an electronic circuit, the variation of current with time is modeled by the differential equation d^2(i)/dt^2 + 36i = dv/dt. Assuming zero initial conditions, determine I as a function of t. (hint: use laplace transforms)
Question 4. Refer to the circuit of Figure 4. R 802 50 uF с vi(t) v.(t)...
Question 4. Refer to the circuit of Figure 4. R 802 50 uF с vi(t) v.(t) Figure 4 a) Draw the circuit in the Laplace domain, and then apply basic circuit theory in the Laplace domain to show that the Laplace transfer function H(s) defined for this system is: HS) V.(5) V (5) sta where a= RC [8 Marks] b) Use Laplace methods to determine the output voltage vo(t) when the input voltage is defined as: v (1) 40(1) The...
thx!!!! Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in...
thx!!!!
Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in Figure 1. What is the value of the steady state gain(s), if any? b) If R1 1, R2 = 2n, C\ = 2- 10-3F, C 1-10-3F, calculate the time constants of the system (if any). c) Find the initial and final values of the unit impulse response of the circuit d) Derive the time-domain expression of the output if the input is the function...
1 4.4-1 The circuit shown in Fig. P4.4-1 has system function given by H(S) = Let...
1 4.4-1 The circuit shown in Fig. P4.4-1 has system function given by H(S) = Let R= 2 and 1+RCS C = 3 and use Laplace transform techniques to solve the following. (a) Find the output y(t) given an initial capaci- tor voltage of y(0%) =3 and an input x(t) u(t). (b) Given an input x(t) = u(t – 3), determine the initial capacitor voltage y(0%) so that the output y(t) is 1 volt at t = 6 seconds. =...
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...
A linear system is governed by the given initial value problem. Find the transfer function H(s)...
A linear system is governed by the given initial value problem. Find the transfer function H(s) for the system and the impulse response function h(t) and give a formula for the solution to the initial value problem. y" - 6y' +34y = g(t); y(O)= 0, y' (O) = 5 Find the transfer function. H(s) = Use the convolution theorem to obtain a formula for the solution to the given initial value problem, where g(t) is piecewise continuous on (0,00) and...
For the circuit shown in Figure 1, determine (a) The transfer function H(s) Vo(s)/V(s) 1 (b)....
For the circuit shown in Figure 1, determine (a) The transfer function H(s) Vo(s)/V(s) 1 (b). The impulse response h(t) given that R,-5Q, R2-2Q, L,-1 mH, and L2 = 2 mH Ri L R2 Figure 1.
Help me do this problem step by step LSM1 Problem (50 pts) Consider a causal continuous-time...
Help me do this problem step by step
LSM1 Problem (50 pts) Consider a causal continuous-time LTI system with input-output relationship dt+)t). (a) Find the transfer function H(s) of the system and specify its ROC. (b) Find the impulse response h(t) of the system. (12 pts) (12 pts) (c) Using the convolution property of the Laplace transform, find the output y(t) of the system in response to the input (t)ut) e2-u(t 1 (26 pts)
a. (10) For the circuit below, draw the s-domain equivalent circuit and show that H(S) = 2 2 . 2321H 0.5F V b. (10) Using Inverse Laplace Transforms, find the impulse response (1) c. (5) Briefly tell me in your own words what an impulse response is. d. (15) For an input, vt) = 2e- Transforms to find vo(t). use Laplace Transforms to find V.(s) and then use Inverse Laplace e. (5) Briefly discuss how convolution could have been used...
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
Question 4. Refer to the circuit of Figure 4. R 802 50 uF с vi(t) v.(t) Figure 4 a) Draw the circuit in the Laplace domain, and then apply basic circuit theory in the Laplace domain to show that the Laplace transfer function H(s) defined for this system is: HS) V.(5) V (5) sta where a= RC [8 Marks] b) Use Laplace methods to determine the output voltage vo(t) when the input voltage is defined as: v (1) 40(1) The...
thx!!!!
Question 3 (5.5 marks) a) Find the transfer function of the electrical circuit shown in Figure 1. What is the value of the steady state gain(s), if any? b) If R1 1, R2 = 2n, C\ = 2- 10-3F, C 1-10-3F, calculate the time constants of the system (if any). c) Find the initial and final values of the unit impulse response of the circuit d) Derive the time-domain expression of the output if the input is the function...
1 4.4-1 The circuit shown in Fig. P4.4-1 has system function given by H(S) = Let R= 2 and 1+RCS C = 3 and use Laplace transform techniques to solve the following. (a) Find the output y(t) given an initial capaci- tor voltage of y(0%) =3 and an input x(t) u(t). (b) Given an input x(t) = u(t – 3), determine the initial capacitor voltage y(0%) so that the output y(t) is 1 volt at t = 6 seconds. =...
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...
A linear system is governed by the given initial value problem. Find the transfer function H(s) for the system and the impulse response function h(t) and give a formula for the solution to the initial value problem. y" - 6y' +34y = g(t); y(O)= 0, y' (O) = 5 Find the transfer function. H(s) = Use the convolution theorem to obtain a formula for the solution to the given initial value problem, where g(t) is piecewise continuous on (0,00) and...
For the circuit shown in Figure 1, determine (a) The transfer function H(s) Vo(s)/V(s) 1 (b). The impulse response h(t) given that R,-5Q, R2-2Q, L,-1 mH, and L2 = 2 mH Ri L R2 Figure 1.
Help me do this problem step by step
LSM1 Problem (50 pts) Consider a causal continuous-time LTI system with input-output relationship dt+)t). (a) Find the transfer function H(s) of the system and specify its ROC. (b) Find the impulse response h(t) of the system. (12 pts) (12 pts) (c) Using the convolution property of the Laplace transform, find the output y(t) of the system in response to the input (t)ut) e2-u(t 1 (26 pts)
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