Explanation Given: The step function is f ( t ) = { sin t , 0 ≤ t < 2 π 0 , t ≥ 2 π . 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 f ( t ) = { sin t , 0 ≤ t < 2 π 0 , t ≥ 2 π

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.3, Problem 60E

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To write: The function f(t)={sint, 0≤t<2π0, t≥2π in terms of unit step function and find the Laplace transformation of it.

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Chapter 4.3, Problem 59E

Chapter 4.3, Problem 61E

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Chapter 4 Solutions

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The function f ( t ) = { sin t , 0 ≤ t < 2 π 0 , t ≥ 2 π in terms of unit step function and find the Laplace transformation of it.

Solution Summary: The author describes the unit step function f(t)=lmathrm

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To write: The function f(t)={sint, 0≤t<2π0, t≥2π in terms of unit step function and find the Laplace transformation of it.

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Chapter 4 Solutions

The function f ( t ) = { sin t , 0 ≤ t &lt; 2 π 0 , t ≥ 2 π in terms of unit step function and find the Laplace transformation of it.

Solution Summary: The author describes the unit step function f(t)=lmathrm

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To write: The function f(t)={sint, 0≤t<2π0, t≥2π in terms of unit step function and find the Laplace transformation of it.

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Chapter 4 Solutions

The function f ( t ) = { sin t , 0 ≤ t < 2 π 0 , t ≥ 2 π in terms of unit step function and find the Laplace transformation of it.