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1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: [Section: 2.2] a. e-a sin oot u(t) b. e-acos at u(t) c. f³u(t)

1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: [Section: 2.2] a. e-a sin oot u(t) b. e-acos at u(t) c. f³u(t)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 80E
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1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: [Section: 2.2] a. e-a sin cot u(t) b. e" cos cot u(t) c. t³u(t) 2. Assuming zero initial conditions, use classical methods to find solutions for the following differential equations: 4. a. dx dt + 5x = 2 cos 3t d²x b. +4 3. Repeat Problem 2, using Laplace transforms. Assume that the forcing functions are zero prior to t = 0_. +3 dx dt + 2x = 2 sin 1 A system is described by the following differential equation: d'y d³x d1³ d²x dx +4 +6 di + 8x Find the expression for the transfer function of the system, Y(s)/X(s). Hint: All initial conditions are assumed to be zero.
Transcribed Image Text:1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions: [Section: 2.2] a. e-a sin cot u(t) b. e" cos cot u(t) c. t³u(t) 2. Assuming zero initial conditions, use classical methods to find solutions for the following differential equations: 4. a. dx dt + 5x = 2 cos 3t d²x b. +4 3. Repeat Problem 2, using Laplace transforms. Assume that the forcing functions are zero prior to t = 0_. +3 dx dt + 2x = 2 sin 1 A system is described by the following differential equation: d'y d³x d1³ d²x dx +4 +6 di + 8x Find the expression for the transfer function of the system, Y(s)/X(s). Hint: All initial conditions are assumed to be zero.
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