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n list Reference f(t) = £ 1 t-1 (n-1)! e-at K cos at 1- e-at sin at (F) 1- cos at Find the transform of the given functions by use of the table. f(t)= e 4t 1 (f) = F(s) 1 S (n = 1,2,3,...) 1 s+a a s(s+ a) S s+a a 2 s+a a² 2 f(t) = £ -¹ (F) at-sin at e-at_ -bt e ae-at-be-bt te - at t-1 e-at e-at (1-at) [(b-a)t + 1] e - at (f)= F(s) s² (s² + a²) b-a (s + a)(s + b) s(a - b) (s + a)(s + b) 1 (s+a)² (n-1)! (s+a)" S (s+a)² s+b (s+a)² f(t) = £¹ (F) sin at - at cos at sin atat cos at e t sin at e t cos at - at sin bt - at cos bt (f) = F(s) 3 2a 2 (s² + a²)² 2as 2 (s²+a²) ² 2as² (s² + a²) ² s²-a² (s² + a²) ² b I (s+a)² + b² s+a (s+a)² + b²

n list Reference f(t) = £ 1 t-1 (n-1)! e-at K cos at 1- e-at sin at (F) 1- cos at Find the transform of the given functions by use of the table. f(t)= e 4t 1 (f) = F(s) 1 S (n = 1,2,3,...) 1 s+a a s(s+ a) S s+a a 2 s+a a² 2 f(t) = £ -¹ (F) at-sin at e-at_ -bt e ae-at-be-bt te - at t-1 e-at e-at (1-at) [(b-a)t + 1] e - at (f)= F(s) s² (s² + a²) b-a (s + a)(s + b) s(a - b) (s + a)(s + b) 1 (s+a)² (n-1)! (s+a)" S (s+a)² s+b (s+a)² f(t) = £¹ (F) sin at - at cos at sin atat cos at e t sin at e t cos at - at sin bt - at cos bt (f) = F(s) 3 2a 2 (s² + a²)² 2as 2 (s²+a²) ² 2as² (s² + a²) ² s²-a² (s² + a²) ² b I (s+a)² + b² s+a (s+a)² + b²

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 2E
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Find the transform of the given function by use of the table.
n list Reference f(t) =< ¹ (F) 1 tn-1 (n-1)! e-at K 1- e-at cos at sin at 1- cos at Find the transform of the given functions by use of the table. f(t)= e 1 1(f) = F(s) 1 S (n=1,2,3,...) 1 s+a a s(s+ a) 2 S 2 +a a 4t 2²+a a² 2 2 s(s² + a²) S f(t) = ¹ (F) at - sin at e-at- e -bt ae-at-be-bt te-at tn-1 e-at e-at (1-at) [(b-a)t + 1] e - at £(f) = F(s) a³ s² (s² + a²) 2 b-a (s + a)(s + b) s(a - b) (s + a)(s + b) 1 (s+a) (n-1)! (s+a)" S (s+a)² s+b (s+a)² f(t) = £¹ (F) sin at - at cos at t sin at sin at + at cos at e t cos at at - at e sin bt cos bt (f) = F(s) 2a³ (s² + a²)² 2 2as 2 + 2as² (s² + ²)² s²-a² 2 2 b (s+a)² + b² s+a (s+a)² +b² X
Transcribed Image Text:n list Reference f(t) =< ¹ (F) 1 tn-1 (n-1)! e-at K 1- e-at cos at sin at 1- cos at Find the transform of the given functions by use of the table. f(t)= e 1 1(f) = F(s) 1 S (n=1,2,3,...) 1 s+a a s(s+ a) 2 S 2 +a a 4t 2²+a a² 2 2 s(s² + a²) S f(t) = ¹ (F) at - sin at e-at- e -bt ae-at-be-bt te-at tn-1 e-at e-at (1-at) [(b-a)t + 1] e - at £(f) = F(s) a³ s² (s² + a²) 2 b-a (s + a)(s + b) s(a - b) (s + a)(s + b) 1 (s+a) (n-1)! (s+a)" S (s+a)² s+b (s+a)² f(t) = £¹ (F) sin at - at cos at t sin at sin at + at cos at e t cos at at - at e sin bt cos bt (f) = F(s) 2a³ (s² + a²)² 2 2as 2 + 2as² (s² + ²)² s²-a² 2 2 b (s+a)² + b² s+a (s+a)² +b² X
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