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Question 4. Consider the system a) b) c) d) Find the Laplace transform of the differential equati...
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...
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).
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y +...
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Question: given a differential equation: a. initial conditions for the plan and input are zero, ...
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
4. Laplace Transform. (15 pts) Find the Laplace Transform of the following signals and sketch the...
4. Laplace Transform. (15 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the form of DO (a) (5 pts)-(t-e*ta(t) + e-8tu(t). Show that X(s) =は,,늚. with ROC of Re(s) >-6. (b) (5 pts)-(t) = M(-t) +Au(-t). (c) (5 pts)-(t) 6(t)-a(-t). (s+6) (s+8)
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation...
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...
I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) =...
I need help with this question of Differential Equation.
Thanks
Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) =...
I need help with this question of Differential Equation.
Thanks
Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform...
(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform (s2 +58 +6)Ý(s) = (s + 2) + (25+5)F(s) where f(s) = What is the zero-input response yzı(t)? yzi(t) = What is the zero-state response yzs(t)? yzs(t) = — What is the output signal y(t)? (t) =.
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...
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).
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
4. Laplace Transform. (15 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the form of DO (a) (5 pts)-(t-e*ta(t) + e-8tu(t). Show that X(s) =は,,늚. with ROC of Re(s) >-6. (b) (5 pts)-(t) = M(-t) +Au(-t). (c) (5 pts)-(t) 6(t)-a(-t). (s+6) (s+8)
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...
I need help with this question of Differential Equation.
Thanks
Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
I need help with this question of Differential Equation.
Thanks
Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform (s2 +58 +6)Ý(s) = (s + 2) + (25+5)F(s) where f(s) = What is the zero-input response yzı(t)? yzi(t) = What is the zero-state response yzs(t)? yzs(t) = — What is the output signal y(t)? (t) =.
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