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Please ignore the hint as we
are only solving part a
3.13, For each homogeneous difference...
Please solve using the general solution method. Do not use Z-Transforms. 3.34. Consider the second-order homogeneous...
Please solve using the general
solution method. Do not use Z-Transforms.
3.34. Consider the second-order homogeneous difference equation with initial conditions yl-1] pi and yl-2 P2. The coefficients a and a2 of the difference equation and the initial values p? and p2 are all real-valued, and will be left as parameters. a. Let z1 and 22 be the roots of the characteristic polynomial. On paper, solve the homogeneous difference equation for the three possibilities for the roots: 1. The roots...
6. Consider the second-order difference equation, 114 pt 16 a. Find the characteristie polynomial and characteristic...
6. Consider the second-order difference equation, 114 pt 16 a. Find the characteristie polynomial and characteristic roots of this system. b. Is this a stable system? Justify your answer mathematically. c. Draw a system diagram for implementing this difference equation using adders, multipliers and time-delays, as needed. d. Find the zero-input solution for initial conditions: l-11-0 and yI-2]--1 in closed- form. e. Find y[l iteratively using the initial conditions given in part f. Find yIl] using the closed form solution...
Discrete math 4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might b...
Discrete math
4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might be e (a) Find a recurrence relation for the number of possible length-n emoji strings that do not contain two consecutive winkey emojis, (b) What are the initial conditions for the recurrence relation? (c) Find a closed-form solution to the recurrence relation you found in part...
Please solve parts (a) and (b) neatly and show problem solving. Ignore reference to part 1, but please still plot the root loci. For the system given in Figure 1 a) Design a PD compensator with the t...
Please solve parts (a) and (b) neatly and show problem solving.
Ignore reference to part 1, but please still plot the root
loci.
For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
write MATLAB scripts to solve differential equations. Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle...
write MATLAB scripts to solve differential equations.
Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
1. (10 points, part I) Consider the following initial boundary value problem lU (la) (1b) (1c) 0L, t> 0 3 cos ( a(x, 0) (a) Classify the partial differential equation (1a) (b) What do the equation...
1. (10 points, part I) Consider the following initial boundary value problem lU (la) (1b) (1c) 0L, t> 0 3 cos ( a(x, 0) (a) Classify the partial differential equation (1a) (b) What do the equations (la)-(1c) model? (Hint: Give an interpretation for the PDE, boundary conditions and intial condition.) c) Use the method of separation of variables to separate the above problem into two sub- problems (one that depends on space and the other only on time) (d) What...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy =...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
questions are connected. please show steps to all Consider the system characterized by the characteristic polynomial...
questions are connected. please show steps to
all
Consider the system characterized by the characteristic polynomial D2+4D+4. (0) Find the zero-input response go(t) of the system, such that vol(o) 0 and o(0) -1. Impulse Response and Zero-State Response 4 Consider the system characterized by the following diferential equation where z() represents the iaut and y(t) the output (D2 +4D+4) y(t) Da(t) (i) Determine the impulse response h(t) of the system. (i) Compute the convolution h r(t) for r(t) eu(t). Hint:...
Part D only plz. Learning Goal: To practice Problem-Solving Strategy for general problems. Two hockey pucks,...
Part D only plz.
Learning Goal:
To practice Problem-Solving Strategy for general problems.
Two hockey pucks, labeled A and B, are initially at rest on a
smooth ice surface and are separated by a distance of 18.0 m .
Simultaneously, each puck is given a quick push, and they begin to
slide directly toward each other. Puck A moves with a speed of 1.50
m/s , and puck B moves with a speed of 2.70 m/s .
What is the...
1 a the system stable. For example, in Chapter 2 we derived the transfer function for the inverte...
1 a the system stable. For example, in Chapter 2 we derived the transfer function for the inverted pendulum, which, for simple values, might be G(s) for which we have bs)1 and as)-s2-1-(s+)(s 1). Suppose we try Dcl (s) = K Istn . The characteristic equation that results for the system is (4.17) This is the problem that Maxwell faced in his study of governors: Under what conditions on the parameters will all the roots of this equation be in...
Please solve using the general
solution method. Do not use Z-Transforms.
3.34. Consider the second-order homogeneous difference equation with initial conditions yl-1] pi and yl-2 P2. The coefficients a and a2 of the difference equation and the initial values p? and p2 are all real-valued, and will be left as parameters. a. Let z1 and 22 be the roots of the characteristic polynomial. On paper, solve the homogeneous difference equation for the three possibilities for the roots: 1. The roots...
6. Consider the second-order difference equation, 114 pt 16 a. Find the characteristie polynomial and characteristic roots of this system. b. Is this a stable system? Justify your answer mathematically. c. Draw a system diagram for implementing this difference equation using adders, multipliers and time-delays, as needed. d. Find the zero-input solution for initial conditions: l-11-0 and yI-2]--1 in closed- form. e. Find y[l iteratively using the initial conditions given in part f. Find yIl] using the closed form solution...
Discrete math
4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might be e (a) Find a recurrence relation for the number of possible length-n emoji strings that do not contain two consecutive winkey emojis, (b) What are the initial conditions for the recurrence relation? (c) Find a closed-form solution to the recurrence relation you found in part...
Please solve parts (a) and (b) neatly and show problem solving.
Ignore reference to part 1, but please still plot the root
loci.
For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
write MATLAB scripts to solve differential equations.
Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
1. (10 points, part I) Consider the following initial boundary value problem lU (la) (1b) (1c) 0L, t> 0 3 cos ( a(x, 0) (a) Classify the partial differential equation (1a) (b) What do the equations (la)-(1c) model? (Hint: Give an interpretation for the PDE, boundary conditions and intial condition.) c) Use the method of separation of variables to separate the above problem into two sub- problems (one that depends on space and the other only on time) (d) What...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
questions are connected. please show steps to
all
Consider the system characterized by the characteristic polynomial D2+4D+4. (0) Find the zero-input response go(t) of the system, such that vol(o) 0 and o(0) -1. Impulse Response and Zero-State Response 4 Consider the system characterized by the following diferential equation where z() represents the iaut and y(t) the output (D2 +4D+4) y(t) Da(t) (i) Determine the impulse response h(t) of the system. (i) Compute the convolution h r(t) for r(t) eu(t). Hint:...
Part D only plz.
Learning Goal:
To practice Problem-Solving Strategy for general problems.
Two hockey pucks, labeled A and B, are initially at rest on a
smooth ice surface and are separated by a distance of 18.0 m .
Simultaneously, each puck is given a quick push, and they begin to
slide directly toward each other. Puck A moves with a speed of 1.50
m/s , and puck B moves with a speed of 2.70 m/s .
What is the...
1 a the system stable. For example, in Chapter 2 we derived the transfer function for the inverted pendulum, which, for simple values, might be G(s) for which we have bs)1 and as)-s2-1-(s+)(s 1). Suppose we try Dcl (s) = K Istn . The characteristic equation that results for the system is (4.17) This is the problem that Maxwell faced in his study of governors: Under what conditions on the parameters will all the roots of this equation be in...
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