Explanation Given: The step function is U ( t − a ) = { 0 , 0 ≤ t < a 1 , a ≤ t ≤ b 1 , t ≥ b . Method 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 of the type, f ( t ) = { g ( t ) , 0 ≤ t < a h ( t ) , t ≥ a . The general piecewise function can be write in terms of the unit step function as f ( t ) = g ( t ) − g ( t ) U ( t − a ) + h ( t ) U ( t − a ) .” Theorem used: “ The second translation theorem: If F ( s ) = L { f ( t ) } and a > 0 , then L { f ( t − a ) U ( t − a ) } = e − a s F ( s ) . The formula for the Laplace transform of constant a is L { a } = a s .” Calculation: Consider the function U ( t − a ) = { 0 , 0 ≤ t < a 1 , a ≤ t ≤ b 1 , t ≥ b

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.3, Problem 61E

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To write: The function U(t−a)={0, 0≤t<a1, a≤t≤b1, t≥b in terms of unit step function and find the Laplace transformation of it.

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Chapter 4.3, Problem 60E

Chapter 4.3, Problem 62E

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Chapter 4 Solutions

Advanced Engineering Mathematics

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The function U ( t − a ) = { 0 , 0 ≤ t < a 1 , a ≤ t ≤ b 1 , t ≥ b in terms of unit step function and find the Laplace transformation of it.

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Chapter 4 Solutions

The function U ( t − a ) = { 0 , 0 ≤ t &lt; a 1 , a ≤ t ≤ b 1 , t ≥ b in terms of unit step function and find the Laplace transformation of it.

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To write: The function U(t−a)={0, 0≤t<a1, a≤t≤b1, t≥b in terms of unit step function and find the Laplace transformation of it.

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Chapter 4 Solutions

The function U ( t − a ) = { 0 , 0 ≤ t < a 1 , a ≤ t ≤ b 1 , t ≥ b in terms of unit step function and find the Laplace transformation of it.