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For each of problem (1 to 3); you are required to deduce the D.E. that best...
Energy approch Q + be be be For each of the given mechanical network, you need...
Energy approch Q + be be be For each of the given mechanical network, you need to use the Lagrange Equation to deduce the D.E. that best describes the network K Ci +Kx f(t) C C K C K C( )Kx Ci,+Kx, Ci C,K(xx) = 0 Ci,Kx, Kx = () K F fit) m C Find the analogy between the parts of problem 2 and problem 3 Problem 3 Problem Problem Input (i) Output (o) WE
Energy approch Q +...
6. Given the D.E: y = 9y' + 20y = r(t) y(0) = 10 y'(O) =...
6. Given the D.E: y = 9y' + 20y = r(t) y(0) = 10 y'(O) = 2 that describes a circuit with input r(t). To find the impulse response of the system, h(t) you would: Y(S) i. Find = H(s) including the initial conditions, then find h(t) by taking the R(S) inverse Laplace transform. ii. Find Y(s) = H(s) with the initial conditions set to zero , then find h(t) by taking R(S) the inverse Laplace transform. iii. Give up...
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...
#4 Problem 1 Find the general solution for the given differential equation Problem 2 Solve the d.e. y(4)2y(3) +2y() 3et +2te- +e-sint. Problem 3 Determine the second, third and fourth derivative o...
#4
Problem 1 Find the general solution for the given differential equation Problem 2 Solve the d.e. y(4)2y(3) +2y() 3et +2te- +e-sint. Problem 3 Determine the second, third and fourth derivative of φ(zo) for the given point xo if y = φ(z) is a solution of the given initial-value problem. ·ry(2) + (1 +z?)y(1) + 31n2(y) = 0; y(1) = 2, y(1)(1)-0 yay) + sina()0: y(0)()a Problem 4 Using power series method provide solution for the d.e. Problem 5 Using...
Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t)...
Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t) and output y(t) Function Generator R, v, (r) y1) Figure 2: RC circuit. (a) (1 point) Sketch the circuit in the phasor domain by replacing the capacitor with its impedance represen- (b) (3 points) Using circuit analysis techniques, show that the frequency response function is Specify the DC gain, K, and the time constant, T, in terms of the parameters R, R, and C...
Problem-4: Find a) the transfer function using “Direct Method” if the input is e(t) and the...
Problem-4: Find a) the transfer function using “Direct Method” if the input is e(t) and the output is eo. For parts b and c, take C = R=1. b) If e(t) = 15, use FVT (if applicable), to determine the steady state value of the zero-state response [(eo)zs]ss. c) If ei(t) = 3cos(2t + 7/3), find steady state response, (eo)ss. * Tivhinois eo Сео
Part I: For each problem, there is only one right answer 1. The model of a...
Part I: For each problem, there is only one right answer 1. The model of a system in the frequency domain is A. the transfer function from the input to the output. B. the differential equation which defines the relation between the input and the output. C. the zero-state response of the system D. None 2. For a system whose input r and output y are related by the differential equation u(0)a30) dr(t) +3r(t) dt dt2 the transfer function from...
Please write and draw the recursive trace, and please explain, thank you! Problem 1. [26 pts]...
Please write and draw the recursive trace, and please explain,
thank you!
Problem 1. [26 pts] Given the Fibonacci numbers, defined as: Fo 0, F1-1, F k Fk2 write or draw the recursive trace of the calculation of the 5th Fibonacci number (Fs 5) with the following Algorithm (which is based on linear recursion) Algorithm Fibonacci Linear (k) Input: a positive integer value k Output: a pair of Fibonacci numbers (F., F..) if k < 2 then R-1 return (R,...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1)...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
Problem 3 Use the 1-DOF EOM at the right to complete this problem. The EOM describes a damped sys...
Problem 3 Use the 1-DOF EOM at the right to complete this problem. The EOM describes a damped system that is being impacted by a force Fh 300N over a period of At 0.01s. Note that s(t) represents the unit impulse function and r is measured in meters. a. Verify that the system is underdamped. b. For zero initial conditions (Zo-Zo = 0), what is the total response r(t)? Plot the response in MATLAB c. For ro1 and o-0, what...
Energy approch Q + be be be For each of the given mechanical network, you need to use the Lagrange Equation to deduce the D.E. that best describes the network K Ci +Kx f(t) C C K C K C( )Kx Ci,+Kx, Ci C,K(xx) = 0 Ci,Kx, Kx = () K F fit) m C Find the analogy between the parts of problem 2 and problem 3 Problem 3 Problem Problem Input (i) Output (o) WE
Energy approch Q +...
6. Given the D.E: y = 9y' + 20y = r(t) y(0) = 10 y'(O) = 2 that describes a circuit with input r(t). To find the impulse response of the system, h(t) you would: Y(S) i. Find = H(s) including the initial conditions, then find h(t) by taking the R(S) inverse Laplace transform. ii. Find Y(s) = H(s) with the initial conditions set to zero , then find h(t) by taking R(S) the inverse Laplace transform. iii. Give up...
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...
#4
Problem 1 Find the general solution for the given differential equation Problem 2 Solve the d.e. y(4)2y(3) +2y() 3et +2te- +e-sint. Problem 3 Determine the second, third and fourth derivative of φ(zo) for the given point xo if y = φ(z) is a solution of the given initial-value problem. ·ry(2) + (1 +z?)y(1) + 31n2(y) = 0; y(1) = 2, y(1)(1)-0 yay) + sina()0: y(0)()a Problem 4 Using power series method provide solution for the d.e. Problem 5 Using...
Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t) and output y(t) Function Generator R, v, (r) y1) Figure 2: RC circuit. (a) (1 point) Sketch the circuit in the phasor domain by replacing the capacitor with its impedance represen- (b) (3 points) Using circuit analysis techniques, show that the frequency response function is Specify the DC gain, K, and the time constant, T, in terms of the parameters R, R, and C...
Problem-4: Find a) the transfer function using “Direct Method” if the input is e(t) and the output is eo. For parts b and c, take C = R=1. b) If e(t) = 15, use FVT (if applicable), to determine the steady state value of the zero-state response [(eo)zs]ss. c) If ei(t) = 3cos(2t + 7/3), find steady state response, (eo)ss. * Tivhinois eo Сео
Part I: For each problem, there is only one right answer 1. The model of a system in the frequency domain is A. the transfer function from the input to the output. B. the differential equation which defines the relation between the input and the output. C. the zero-state response of the system D. None 2. For a system whose input r and output y are related by the differential equation u(0)a30) dr(t) +3r(t) dt dt2 the transfer function from...
Please write and draw the recursive trace, and please explain,
thank you!
Problem 1. [26 pts] Given the Fibonacci numbers, defined as: Fo 0, F1-1, F k Fk2 write or draw the recursive trace of the calculation of the 5th Fibonacci number (Fs 5) with the following Algorithm (which is based on linear recursion) Algorithm Fibonacci Linear (k) Input: a positive integer value k Output: a pair of Fibonacci numbers (F., F..) if k < 2 then R-1 return (R,...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
Problem 3 Use the 1-DOF EOM at the right to complete this problem. The EOM describes a damped system that is being impacted by a force Fh 300N over a period of At 0.01s. Note that s(t) represents the unit impulse function and r is measured in meters. a. Verify that the system is underdamped. b. For zero initial conditions (Zo-Zo = 0), what is the total response r(t)? Plot the response in MATLAB c. For ro1 and o-0, what...
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