Problem 2 (graded) Section 6.5: Impulse Fun Xedfinity.com/assessments/5f9094725db5a60ee0b5b431?start=falseConsider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function:a" – 6x' = 8(t – 4),x(0) = 7, 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 x(t).x(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 0

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Description: Problem 2 (graded) Section 6.5: Impulse Fun Xedfinity.com/assessments/5f9094725db5a60ee0b5b431?start=falseConsider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function:a"

Given, x''-6x'=δ(t-4), x(0)=7, x'(0)=0. a). We know that,…

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Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: æ" – 6x' = 8(t – 4), æ(0) = 7, 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 æ(t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4.

Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: æ" – 6x' = 8(t – 4), æ(0) = 7, 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 æ(t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Problem 2

(graded) Section 6.5: Impulse Fun X
edfinity.com/assessments/5f9094725db5a60ee0b5b431?start=false
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function:
a" – 6x' = 8(t – 4),
x(0) = 7, 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 x(t).
x(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 0 <t < 4,
x(t) =
if 4 <t < .
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