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Determine the Laplace transform of the given function. a) f(t) = 2+1¹ c) f(t)=sinh(5t) e) f(t) = cos² (5t) b) f(t) = 3 sin(2t) +5e³t d) f(t) = sint cost f) f(t)= te' +2 sin² (31)

Determine the Laplace transform of the given function. a) f(t) = 2+1¹ c) f(t)=sinh(5t) e) f(t) = cos² (5t) b) f(t) = 3 sin(2t) +5e³t d) f(t) = sint cost f) f(t)= te' +2 sin² (31)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
2a
## Laplace Transform Problems Determine the Laplace transform of the given function: ### Functions: a) \( f(t) = 2 + t^4 \) b) \( f(t) = 3\sin(2t) + 5e^{3t} \) c) \( f(t) = \sinh(5t) \) d) \( f(t) = \sin t \cos t \) e) \( f(t) = \cos^2(5t) \) f) \( f(t) = te^t + 2\sin^2(3t) \) ### Explanation: The above functions are provided for determining their Laplace transforms using standard Laplace transform tables and properties such as linearity, shifts, and derivatives. Understanding these functions and their transformations is crucial for solving differential equations in engineering and physics. Each function represents a different mathematical expression involving exponential, trigonometric, or hyperbolic functions, making them suitable for exploring the breadth of Laplace transforms.
Transcribed Image Text:## Laplace Transform Problems Determine the Laplace transform of the given function: ### Functions: a) \( f(t) = 2 + t^4 \) b) \( f(t) = 3\sin(2t) + 5e^{3t} \) c) \( f(t) = \sinh(5t) \) d) \( f(t) = \sin t \cos t \) e) \( f(t) = \cos^2(5t) \) f) \( f(t) = te^t + 2\sin^2(3t) \) ### Explanation: The above functions are provided for determining their Laplace transforms using standard Laplace transform tables and properties such as linearity, shifts, and derivatives. Understanding these functions and their transformations is crucial for solving differential equations in engineering and physics. Each function represents a different mathematical expression involving exponential, trigonometric, or hyperbolic functions, making them suitable for exploring the breadth of Laplace transforms.
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