only HANDWRITTEN answer needed ( NOT TYPED)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
only HANDWRITTEN answer needed ( NOT TYPED)
![Consider the the following piecewise function.
f(t) =
0
et
t< 0
0 < t <3
t> 3
a. Convert this function into a single expression using Heaviside functions.
f(t) =
H(t-3)+e^(t)*H(t)-e^(t)*H(t-3)
Your last answer was interpreted as follows:
H (t − 3) + e¹ H (t) + (−e¹) H (t − 3)
The variables found in your answer were: [t]
b. Rewrite this expression to consist of terms of the form g(t – a)H(t – a). Note: you should put
brackets around each (t – a) term in your answer to clearly group them together.
f(t) = H(t-3)+e^(t-3)*H(t-3)-e^(t)*H(t-3)
Your last answer was interpreted as follows:
H (t− 3) + e²-³ H (t − 3) + (−e¹) H (t − 3)
The variables found in your answer were: [4]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe76f9d10-ca18-4feb-b110-ce79e013d4c0%2Fa0504de7-36f6-44b6-a258-6dd49828a9b7%2Fp6627s_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the the following piecewise function.
f(t) =
0
et
t< 0
0 < t <3
t> 3
a. Convert this function into a single expression using Heaviside functions.
f(t) =
H(t-3)+e^(t)*H(t)-e^(t)*H(t-3)
Your last answer was interpreted as follows:
H (t − 3) + e¹ H (t) + (−e¹) H (t − 3)
The variables found in your answer were: [t]
b. Rewrite this expression to consist of terms of the form g(t – a)H(t – a). Note: you should put
brackets around each (t – a) term in your answer to clearly group them together.
f(t) = H(t-3)+e^(t-3)*H(t-3)-e^(t)*H(t-3)
Your last answer was interpreted as follows:
H (t− 3) + e²-³ H (t − 3) + (−e¹) H (t − 3)
The variables found in your answer were: [4]
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