Verify that u' (t – a) = 8(t – a) by solving the problemx' = 8(t – a); x (0) = 0to obtain x (1) = u(t – a).

Answered: Verify that u' (t – a) = 8(t – a) by…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Verify that u' (t – a) = 8(t – a) by solving the problem
x' = 8(t – a); x (0) = 0
to obtain x (1) = u(t – a).

Expert Solution

Step 1

What is Laplace Transformation:

Laplace transformation is crucial for control system design. Laplace transforms must be applied to a number of functions in order to analyse the control system. The characteristics of the Laplace transform and the inverse Laplace transformation are both employed to analyse the dynamic control system. It is an integral transformation.

Given:

Given initial value problem is

$x' = δ (t - a)$

With initial condition $x (0) = 0$ .

To Determine:

We verify that $u' (t - a) = δ (t - a)$ by solving the initial value problem.