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Determine the inverse Laplace transform of the function below. 16 s² +25 Click here to view the table of Laplace transforms

Determine the inverse Laplace transform of the function below. 16 s² +25 Click here to view the table of Laplace transforms

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
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Determine the inverse Laplace transform of the function below. 16 s²+25 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 16 *{*}-0 s² +25 L = Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = CL{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) = s^ L{f}(s) - s^−¹f(0) -sª-2f'(0) - ... -f(n-1) (0) S dn dsn L {t¹f(t)} (s) = ( − 1)n- -(L{f}(s)) L-1 £¯¹ {F₁+F₂} = £¯¹{F₁} + £¯¹ {F2} L¹{CF} = CL¹{F} Table of Laplace Transforms - X f(t) 1 eat t", n=1,2,... sin bt cos bt eat,n=1,2,.... eat eat sin bt cos bt F(s) = L{f}(s) 1 ,S> 0 S 1 s-a n! sn +1: ,S> 0 ,S> 0 b s² + b² 2 S s² + b² n! (s-a)n+1 b S> 0 ,S> 0 ,s> a s> a (s-a)² + b² s-a (s-a)² + b²¹ ,s> a
Transcribed Image Text:Determine the inverse Laplace transform of the function below. 16 s²+25 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 16 *{*}-0 s² +25 L = Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = CL{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) = s^ L{f}(s) - s^−¹f(0) -sª-2f'(0) - ... -f(n-1) (0) S dn dsn L {t¹f(t)} (s) = ( − 1)n- -(L{f}(s)) L-1 £¯¹ {F₁+F₂} = £¯¹{F₁} + £¯¹ {F2} L¹{CF} = CL¹{F} Table of Laplace Transforms - X f(t) 1 eat t", n=1,2,... sin bt cos bt eat,n=1,2,.... eat eat sin bt cos bt F(s) = L{f}(s) 1 ,S> 0 S 1 s-a n! sn +1: ,S> 0 ,S> 0 b s² + b² 2 S s² + b² n! (s-a)n+1 b S> 0 ,S> 0 ,s> a s> a (s-a)² + b² s-a (s-a)² + b²¹ ,s> a
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