Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Determine the inverse Laplace transform of the function below. 4s +37 s² +6s+34 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-1 4s +37 $²2+6s+34 Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c£{f} for any constant c Leatf(t)} (s) = L{f}(s-a) L {f'} (s) = s£{f}(s) - f(0) L {f'' (s) = s² L{f}(s) - sf(0) - f'(0) L {f(n)} (s) = s£{f}(s)-s-1f(0)-s-2f'(0)-... -f(n-1) (0) dn L {t^f(t)} (s) = (-1)^- dsn = £¯¹ {F₁} + £¯ £¯1{F₁+F2} L1¹{CF} = c£¯¹{F} (L{f}(s)) Table of Laplace Transforms X f(t) 1 eat t", n=1,2,... sin bt cos bt eat,n=1,2,.... eat sin bt eat cos bt F(s) = L{f}(s) 1 s 1 s-a n! Sn+18>0 ,S>0 ,S> 0 b s² + b² ,s > 0 S s²+ b² n! (s-a)n +1 b ,S>0 .s> a (s-a)² + b² s-a (s-a)² + b² .s> a .s> a

Determine the inverse Laplace transform of the function below. 4s +37 s² +6s+34 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-1 4s +37 $²2+6s+34 Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c£{f} for any constant c Leatf(t)} (s) = L{f}(s-a) L {f'} (s) = s£{f}(s) - f(0) L {f'' (s) = s² L{f}(s) - sf(0) - f'(0) L {f(n)} (s) = s£{f}(s)-s-1f(0)-s-2f'(0)-... -f(n-1) (0) dn L {t^f(t)} (s) = (-1)^- dsn = £¯¹ {F₁} + £¯ £¯1{F₁+F2} L1¹{CF} = c£¯¹{F} (L{f}(s)) Table of Laplace Transforms X f(t) 1 eat t", n=1,2,... sin bt cos bt eat,n=1,2,.... eat sin bt eat cos bt F(s) = L{f}(s) 1 s 1 s-a n! Sn+18>0 ,S>0 ,S> 0 b s² + b² ,s > 0 S s²+ b² n! (s-a)n +1 b ,S>0 .s> a (s-a)² + b² s-a (s-a)² + b² .s> a .s> a

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 51E
See similar textbooks
icon
Related questions
Question
Determine the inverse Laplace transform of the function below. 4s +37 s² +6s+34 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. £2-1 4s +37 s² +6s+34 =0 = Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c£{f} for any constant c L{eªtf(t)} (s) = L{f}(s − a) ( ) L {f'} (s) = s£{f}(s) - f(0) L {f''} (s) = s²L{f}(s) - sf(0) - f'(0) L {f(n)} (s) = s¹L{f}(s) - s^-1f(0) - s^-2f'(0) -... f(n-1) (0) L{tf(t)} (s) = (-1) (L{f}(s)) dn dsn 2-1 £¯¹ {F₁+F₂} = £¯¹ {F₁} + £¯¹ {F2} 2-1 L¹ {CF} = CL¹{F} Table of Laplace Transforms - X f(t) 1 eat t,n=1,2,... sin bt cos bt et, n=1,2,... eat sin bt eat cos bt F(s) = L{f}(s) 1 S 1 ,S> 0 ,S> 0 7 s-a nl sn +1 1 b s² + b² S>0 S> 0 S s² + b²' n! (s-a)n +1 b (s-a)² + b² s-a (s-a)² + b² ,S> O 0 s> a ,S> a s> ,s> a
Transcribed Image Text:Determine the inverse Laplace transform of the function below. 4s +37 s² +6s+34 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. £2-1 4s +37 s² +6s+34 =0 = Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c£{f} for any constant c L{eªtf(t)} (s) = L{f}(s − a) ( ) L {f'} (s) = s£{f}(s) - f(0) L {f''} (s) = s²L{f}(s) - sf(0) - f'(0) L {f(n)} (s) = s¹L{f}(s) - s^-1f(0) - s^-2f'(0) -... f(n-1) (0) L{tf(t)} (s) = (-1) (L{f}(s)) dn dsn 2-1 £¯¹ {F₁+F₂} = £¯¹ {F₁} + £¯¹ {F2} 2-1 L¹ {CF} = CL¹{F} Table of Laplace Transforms - X f(t) 1 eat t,n=1,2,... sin bt cos bt et, n=1,2,... eat sin bt eat cos bt F(s) = L{f}(s) 1 S 1 ,S> 0 ,S> 0 7 s-a nl sn +1 1 b s² + b² S>0 S> 0 S s² + b²' n! (s-a)n +1 b (s-a)² + b² s-a (s-a)² + b² ,S> O 0 s> a ,S> a s> ,s> a
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS