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Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' + x = 9+5(t – 5), x(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{2(t)}(s) = b. Obtain the solution z(t). (t) = c. Express the solution as a piecewise-defined function and think about what happens to the...
Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' +2=1 + (t - 2), X(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{a(t)}(8) = b. Obtain the solution z(t). (t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of...
Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 2x' = (t – 4), x(0) = 4, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). x(t) = c. Express the solution as a piecewise-defined function and think about what...
Consider the following initial value problem, in which an input of large amplitude and short duration...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" + 91- x = 318(t – 3), x(0) = 0, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). X(t) = c. Express the solution as a piecewise-defined function and think about...
Consider the following initial value problem, in which an input of large amplitude and short...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.y′+y=7+δ(t−1),y(0)=0.Find the Laplace transform of the solution. Y(s)=L{y(t)}=Obtain the solution y(t). y(t)=Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=1. y(t)= { if 0≤t<1, if 1≤t<∞.
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has bee...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
(1 point) Consider the following initial value problem, in which an input of large amplitude and...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 167²y = 418(t – 4), y(O) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} = b. Obtain the solution y(t). yt) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t =...
(1 point) Consider the following initial value problem, in which an input of large amplitude and...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. a. Find the Laplace transform of the solution. b. Obtain the solution y(t) y(t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t-5 y(f)- if5<t<oo.
(1 point) Consider the following initial value problem, in which an input of large amplitude and...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function a Find the Laplace transform of the solution. b. Obtain the solution y(t) u(t)- C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution att 1 İf 0 < t < 1, y(t) if 1 t<oo.
(2 points) Consider the following initial value problem, in which an input of large amplitude and...
(2 points) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. yy1+(t-4), y(0)0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)) = b. Obtain the solution y(t) C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. if 0st<4, y(t) if 4t< o0.
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' + x = 9+5(t – 5), x(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{2(t)}(s) = b. Obtain the solution z(t). (t) = c. Express the solution as a piecewise-defined function and think about what happens to the...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' +2=1 + (t - 2), X(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{a(t)}(8) = b. Obtain the solution z(t). (t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 2x' = (t – 4), x(0) = 4, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). x(t) = c. Express the solution as a piecewise-defined function and think about what...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" + 91- x = 318(t – 3), x(0) = 0, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). X(t) = c. Express the solution as a piecewise-defined function and think about...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 167²y = 418(t – 4), y(O) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} = b. Obtain the solution y(t). yt) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t =...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. a. Find the Laplace transform of the solution. b. Obtain the solution y(t) y(t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t-5 y(f)- if5<t<oo.
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function a Find the Laplace transform of the solution. b. Obtain the solution y(t) u(t)- C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution att 1 İf 0 < t < 1, y(t) if 1 t<oo.
(2 points) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. yy1+(t-4), y(0)0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)) = b. Obtain the solution y(t) C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. if 0st<4, y(t) if 4t< o0.
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