Find the Laplace transform F(s) of f(t) = et4u(t – 4) F(8):
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![**Problem Statement: Finding the Laplace Transform**
Find the Laplace transform \( F(s) \) of the function \( f(t) = e^{t-4} u(t - 4) \).
**Solution:**
\[ F(s) = \]
**Explanation:**
The function \( f(t) = e^{t-4} u(t - 4) \) involves an exponential term and the unit step function \( u(t-4) \), which shifts the function to the right by 4 units. The Laplace transform of this type of function is obtained using the shifting property of the Laplace transform.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16510717-aebe-4647-9d51-4dea6e47545d%2Fb36e76d9-af57-4e0e-8430-348e623b2b43%2Fatjrm1w_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Finding the Laplace Transform**
Find the Laplace transform \( F(s) \) of the function \( f(t) = e^{t-4} u(t - 4) \).
**Solution:**
\[ F(s) = \]
**Explanation:**
The function \( f(t) = e^{t-4} u(t - 4) \) involves an exponential term and the unit step function \( u(t-4) \), which shifts the function to the right by 4 units. The Laplace transform of this type of function is obtained using the shifting property of the Laplace transform.
![**Problem: Finding the Laplace Transform**
Calculate the Laplace transform \( F(s) \) of the function \( f(t) = 2t u(t - 7) \).
**Solution:**
\[ F(s) = \]
In this expression, \( u(t - 7) \) is the Heaviside step function, which shifts the function \( 2t \) by 7 units to the right on the time axis. The challenge is to find the corresponding \( F(s) \) for this time-shifted function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16510717-aebe-4647-9d51-4dea6e47545d%2Fb36e76d9-af57-4e0e-8430-348e623b2b43%2Fln84xn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Finding the Laplace Transform**
Calculate the Laplace transform \( F(s) \) of the function \( f(t) = 2t u(t - 7) \).
**Solution:**
\[ F(s) = \]
In this expression, \( u(t - 7) \) is the Heaviside step function, which shifts the function \( 2t \) by 7 units to the right on the time axis. The challenge is to find the corresponding \( F(s) \) for this time-shifted function.
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