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PRACTICE PROBLEMS CHAPTER 6 AND 7 I. Laplace Transform 1. Find the Laplace transform of the following functions. (a) f t =sin 2t cos 2t (b) f t =cos2 3t (c) f t =te2tsin 3t (d) f t = t 3 u7 t (e) f t =t2u 3 t (f) f t ={1, if 0≤t 2, t2−4t 4, if t≥2 (g) f t ={t, if 0≤t 3,
Laplace Transform Practice Problems (Answers on the last page) (A) Continuous Examples (no step functions): Compute the Laplace transform of the given function.
1. Use the rules and formulas to nd the Laplace transform of e t(t2 + 1): 2. Let f(t) = e t cos(3t): (a) From the rules and tables, what is F(s) = L[f(t)]? (b) Compute the derivative f0(t) and its Laplace transform. Verify the t-derivative rule in this case. 3. Use the Laplace transform to nd the unit impulse response and the unit step response
Laplace Transforms – Practice Problems . 1. Compute Transforms Directly a. t. 2. b. e. −5. t. c. sin. at. d. sinh3. t. 2. Use Properties and Basic Transforms a. Find Laplace Transform i. sin(5 2) t + ii. te. 2. t. iii. et. −. t. sin2 iv. tt. sin v. tH t ( 1)− vi. sin ( ) 2. tHt. π ⋅− vii. 0. cos2. t. ∫. e udu. −−. tu. b. Find ...
† Know how to use all of the Laplace transform formulas developed in Section 3.1 to be able to compute the Laplace transform of elementary functions. † Know how to use partial fraction decompositions to be able to compute the inverse Laplace
MAT 275 CHAPTER 6, 7 PRACTICE PROBLEMS (Material from earlier sections are on previous reviews) Given Laplace Transform Table: 6.3. Step Functions 1. Find the Laplace transform of the following functions. (a) ( ( )= +3 7 ) (b) ( )=2 3 (c) ( )={1, 0≤ <2 2−4 +4, ≥2
WORKSHEET: LAPLACE TRANSFORM. Problem 1. Find the Laplace transform for. 1 0 t < 4. (a) f(t) = 3 4 t < 5 0 5 t < 1. 0 t < 1. (c). f(t) = 0 1 t < 1. Part (a) Solutions: First rewrite f(t) 0 t < 2. (b). f(t) = (t 0 2 t < 1 (sin(t) 0 t < ⇡. (d). f(t) = cos(t) ⇡ t < 1. terms of heavyside function. f(t) = 1 + (3. 1) + (0.
