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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 How)...
A linear system is governed by the given initial value problem. Find the transfer function How) for the system and the impune response function hil) and give a fomida for the solution to the initial value problem. y'-' +17y=(t): y0) = 0, y(0) - 4 Find the transfer function Find the impulse response function. Give a formula for the solution to the initial value problem using as the contin variable
For full credit, you must show all work and box answers 1. If functions f and g are piecewise con...
For full credit, you must show all work and box answers 1. If functions f and g are piecewise continuous on the interval [0, oo), then the convolution of f and g is a function defined by the integral The Convolution Theorem (theorem 7.4.2 in your book and formula 6 in your table) states: If j(t) and g) are piecewise continuous on [0, oo) and of exponential order, then We are going to use convolution to solve y"-y,-t-e-,, y(0)-0, y'(0)-0....
Use the convolution theorem to obtain a formula for the solution to the initial value problem....
Use the convolution theorem to obtain a formula for the solution
to the initial value problem.
y ′′ + y = g, y(0) = 0, y′ (0) = 1 , where g = g(t) is a given
function.
1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, where g = g(t) is a given function.
Problem C and E please. 3. Find a formula for the solution of the initial value...
Problem C and E please.
3. Find a formula for the solution of the initial value problem. (a) y" + 3y' + y = f(t), y(0) = 0, y'(0) = 0 (b) y'' + 4y = f(t), y(0) = 0, y'(0) = 0 (c) y" + 2y' + y = f(t), y(0) = 0, y'(O) = 0 (d) y" + k2y = f(t), y(0) = 1, y'(0) = -1 (e) y" + 6y' + 9y = f(t), y(0) = 0,...
Please help both questions, thanks (1 point) Let g(t) = e2 a Solve the initial value...
Please help both questions, thanks
(1 point) Let g(t) = e2 a Solve the initial value problem 4 – 2 = g(t), using the technique of integrating factors. (Do not use Laplace transforms.) y(0) = 0, (t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem 6' - 24 = 8(t), (0) = 0. $(t) = c. Evaluate the convolution integral (6 + 9)(t) = Sølt – w)g(w) dw, and compare the resulting...
6.[10] Find the solution to the vibrating string problem governed by the given initial-boundary value problem:...
6.[10] Find the solution to the vibrating string problem governed by the given initial-boundary value problem: 9uxx = Utt 0<x< 1, t> 0 u(0,t) = 0) = u(tt,t), t> 0 u(x,0) = sin 4x + 7 sin 5x, 0<x< 1 uz (3,0) = { X, 0 < x < 1/2 r/2 < x <
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system 2. Consider a linear time-invariant system with transfer f...
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
where h is the Use the Laplace transform to solve the following initial value problem: y"+y...
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. L{y(t)}(s) = b. Express the solution y(t) as the...
Please solve both questions please. Solve the given initial value problem. y'"' + 11y'' + 38y'...
Please solve both questions please.
Solve the given initial value problem. y'"' + 11y'' + 38y' + 40y = 0 y(0)= 0, y'(0) = 10, y''(O) = - 72 y(x) = Find a general solution for the given differential equation with x as the independent variable. y(4) + 6y'' +9y = 0 A general solution with x as the independent variable is y(x) =
Solve 6y" - 6y' + 9y = t^2e^3t .... y(0)=0 & y'(0)=0 An initial Value Problem...
Solve 6y" - 6y' + 9y = t^2e^3t .... y(0)=0 & y'(0)=0
An initial Value Problem Sove: y'-6y +9y=t&t, y(O) = 0 , Y'()=0 Please Solve this IVP.
A linear system is governed by the given initial value problem. Find the transfer function How) for the system and the impune response function hil) and give a fomida for the solution to the initial value problem. y'-' +17y=(t): y0) = 0, y(0) - 4 Find the transfer function Find the impulse response function. Give a formula for the solution to the initial value problem using as the contin variable
For full credit, you must show all work and box answers 1. If functions f and g are piecewise continuous on the interval [0, oo), then the convolution of f and g is a function defined by the integral The Convolution Theorem (theorem 7.4.2 in your book and formula 6 in your table) states: If j(t) and g) are piecewise continuous on [0, oo) and of exponential order, then We are going to use convolution to solve y"-y,-t-e-,, y(0)-0, y'(0)-0....
Use the convolution theorem to obtain a formula for the solution
to the initial value problem.
y ′′ + y = g, y(0) = 0, y′ (0) = 1 , where g = g(t) is a given
function.
1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, where g = g(t) is a given function.
Problem C and E please.
3. Find a formula for the solution of the initial value problem. (a) y" + 3y' + y = f(t), y(0) = 0, y'(0) = 0 (b) y'' + 4y = f(t), y(0) = 0, y'(0) = 0 (c) y" + 2y' + y = f(t), y(0) = 0, y'(O) = 0 (d) y" + k2y = f(t), y(0) = 1, y'(0) = -1 (e) y" + 6y' + 9y = f(t), y(0) = 0,...
Please help both questions, thanks
(1 point) Let g(t) = e2 a Solve the initial value problem 4 – 2 = g(t), using the technique of integrating factors. (Do not use Laplace transforms.) y(0) = 0, (t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem 6' - 24 = 8(t), (0) = 0. $(t) = c. Evaluate the convolution integral (6 + 9)(t) = Sølt – w)g(w) dw, and compare the resulting...
6.[10] Find the solution to the vibrating string problem governed by the given initial-boundary value problem: 9uxx = Utt 0<x< 1, t> 0 u(0,t) = 0) = u(tt,t), t> 0 u(x,0) = sin 4x + 7 sin 5x, 0<x< 1 uz (3,0) = { X, 0 < x < 1/2 r/2 < x <
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. L{y(t)}(s) = b. Express the solution y(t) as the...
Please solve both questions please.
Solve the given initial value problem. y'"' + 11y'' + 38y' + 40y = 0 y(0)= 0, y'(0) = 10, y''(O) = - 72 y(x) = Find a general solution for the given differential equation with x as the independent variable. y(4) + 6y'' +9y = 0 A general solution with x as the independent variable is y(x) =
Solve 6y" - 6y' + 9y = t^2e^3t .... y(0)=0 & y'(0)=0
An initial Value Problem Sove: y'-6y +9y=t&t, y(O) = 0 , Y'()=0 Please Solve this IVP.
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