Explanation Given: The provided step function is f ( t ) = { 0 , 0 ≤ t < 1 1 , 1 ≤ t < 2 2 , 2 ≤ t < 3 3 , 3 ≤ t < 4 . Concept used: The unit step function U ( t − a ) is defined as, U ( t − a ) = { 0 , 0 ≤ t < a 1 , t ≥ a The general piecewise-defined function is of the type, f ( t ) = { g ( t ) , 0 ≤ t < a h ( t ) , t ≥ a where, it is written as f ( t ) = g ( t ) − g ( t ) U ( t − a ) + h ( t ) U ( t − a ) . The Laplace transformation of constant L { a } = a s . Second translation theorem The second translation theorem is given as follows. If F ( s ) = L { f ( t ) } and a > 0 then L { f ( t − a ) U ( t − a ) } = e − a s F ( s ) . Calculation: The provided function f ( t ) = { 0 , 0 ≤ t < 1 1 , 1 ≤ t < 2 2 , 2 ≤ t < 3 3 , 3 ≤ t < 4 . Compare above function with the general piecewise function and obtain the values as follows

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.3, Problem 62E

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The Laplace transformation of provided function and also write the given function in terms of unit step function.

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Chapter 4.3, Problem 61E

Chapter 4.3, Problem 63E

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Chapter 4 Solutions

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The Laplace transformation of provided function and also write the given function in terms of unit step function.

Solution Summary: The author explains the Laplace transformation of provided function and also write the given function in terms of unit step function.

The Laplace transformation of provided function and also write the given function in terms of unit step function.

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Chapter 4 Solutions