Homework Answers
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x(t) and y(t) satisfy the following system of differential equations: de todo-y=0, de+ 5y =e-6t, sc(0)=y(0)=0....
x(t) and y(t) satisfy the following system of differential equations: di +827-y=0, +3y=e-4t, x(0)=y(0)=0. Find the...
x(t) and y(t) satisfy the following system of differential equations: di +827-y=0, +3y=e-4t, x(0)=y(0)=0. Find the Laplace transform of y(t) Your answer should be expressed as a function of s using the correct syntax.
What is the Laplace transform of: f(t)=-8sin(6t)+9H(t-27)cos(6t)? Your answer should be expressed as a function of...
What is the Laplace transform of: f(t)=-8sin(6t)+9H(t-27)cos(6t)? Your answer should be expressed as a function of s using the correct syntax. Note that the correct syntax for it is Pi. For example: (2-3*exp(-Pi*s)/(s^2+1) Laplace transform is F(s) = Skipped
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
The functions æ(t), y(t) satisfy the system of equations x (t) = -3 x (t) –...
The functions æ(t), y(t) satisfy the system of equations x (t) = -3 x (t) – y(t) ft y(t) = 5 x (t) – y(t) and the initial conditions x(0) = 1 and y(0) = -1. Suppose that the Laplace transforms of x(t), y(t) are respectively X(s), Y(s). By forming algebraic equations in X(s), Y(s)., find and the enter the function X(s), Y(s) below in maple syntax. X(s) = Y(s) =
The functions (t), y(t) satisfy the system of equations dt d v052(01(0 3y(t) and the initial...
The functions (t), y(t) satisfy the system of equations dt d v052(01(0 3y(t) and the initial conditions (0)1 and y(0)4 Suppose that the Laplace transforms of z(t), y(t) are respectively X(s), Y(8). By forming algebraic equations in X(s), Y(8). find and the enter the function X(s), Y(8) below syntax. X(s) Y(s)
Consider the following initial value problem. y′ + 5y = { 0 t ≤ 1 10...
Consider the following initial value problem.
y′ + 5y =
{
0
t ≤ 1
10
1 ≤ t < 6
0
6 ≤ t < ∞
y(0) = 4
(a)
Find the Laplace transform of the right hand side of the above
differential equation.
(b)
Let y(t) denote the solution to the above
differential equation, and let Y((s) denote the
Laplace transform of y(t). Find
Y(s).
(c)
By taking the inverse Laplace transform of your answer to (b),
the...
2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) =...
2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for the input x(t) = 24 cos(6t) u(t) by using Laplace Transform. how t6yce) = . _ x06) y(t) =
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1)...
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for...
Question 1 (1 mark) Attempt 1 What is the Fourier transform of j(t)-e-3tcos(6t)H(t)? Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) Questi...
Question 1 (1 mark) Attempt 1 What is the Fourier transform of j(t)-e-3tcos(6t)H(t)? Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w)
Question 1 (1 mark) Attempt 1 What is the Fourier transform of j(t)-e-3tcos(6t)H(t)? Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w)
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0)...
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
x(t) and y(t) satisfy the following system of differential equations: di +827-y=0, +3y=e-4t, x(0)=y(0)=0. Find the Laplace transform of y(t) Your answer should be expressed as a function of s using the correct syntax.
What is the Laplace transform of: f(t)=-8sin(6t)+9H(t-27)cos(6t)? Your answer should be expressed as a function of s using the correct syntax. Note that the correct syntax for it is Pi. For example: (2-3*exp(-Pi*s)/(s^2+1) Laplace transform is F(s) = Skipped
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
The functions æ(t), y(t) satisfy the system of equations x (t) = -3 x (t) – y(t) ft y(t) = 5 x (t) – y(t) and the initial conditions x(0) = 1 and y(0) = -1. Suppose that the Laplace transforms of x(t), y(t) are respectively X(s), Y(s). By forming algebraic equations in X(s), Y(s)., find and the enter the function X(s), Y(s) below in maple syntax. X(s) = Y(s) =
The functions (t), y(t) satisfy the system of equations dt d v052(01(0 3y(t) and the initial conditions (0)1 and y(0)4 Suppose that the Laplace transforms of z(t), y(t) are respectively X(s), Y(8). By forming algebraic equations in X(s), Y(8). find and the enter the function X(s), Y(8) below syntax. X(s) Y(s)
Consider the following initial value problem.
y′ + 5y =
{
0
t ≤ 1
10
1 ≤ t < 6
0
6 ≤ t < ∞
y(0) = 4
(a)
Find the Laplace transform of the right hand side of the above
differential equation.
(b)
Let y(t) denote the solution to the above
differential equation, and let Y((s) denote the
Laplace transform of y(t). Find
Y(s).
(c)
By taking the inverse Laplace transform of your answer to (b),
the...
2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for the input x(t) = 24 cos(6t) u(t) by using Laplace Transform. how t6yce) = . _ x06) y(t) =
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for...
Question 1 (1 mark) Attempt 1 What is the Fourier transform of j(t)-e-3tcos(6t)H(t)? Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w)
Question 1 (1 mark) Attempt 1 What is the Fourier transform of j(t)-e-3tcos(6t)H(t)? Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w)
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
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