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s11_mthsc208_hw14

# s11_mthsc208_hw14 - MthSc 208 Spring 2011(Differential...

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MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 14 Due Thursday, March 31st, 2011 (1) Find the inverse Laplace transform of the following functions. (a) Y ( s ) = 2 3 - 5 s (b) Y ( s ) = 1 s 2 + 4 (c) Y ( s ) = 5 s s 2 + 9 (d) Y ( s ) = 3 s 2 (e) Y ( s ) = 3 s + 2 s 2 + 25 (f) Y ( s ) = 2 - 5 s s 2 + 9 (g) Y ( s ) = s ( s + 2) 2 + 4 (h) Y ( s ) = 3 s + 2 s 2 + 4 s + 29 (i) Y ( s ) = 2 s - 2 ( s - 4)( s + 2) (j) Y ( s ) = 3 s 2 + s + 1 ( s - 2)( s 2 + 1) (2) Use the Laplace transform to solve the following initial value problems. (a) y 0 - 4 y = e - 2 t t 2 , y (0) = 1 (b) y 00 - 9 y = - 2 e t , y (0) = 0 , y 0 (0) = 1 (3) Find the Laplace transform of the given functions. (a) 3 H ( t - 2) (b) ( t - 2) H ( t - 2) (c) e 2( t - 1) H ( t - 1) (d) H ( t - π/ 4) sin 3( t - π/ 4) (e) t 2 H ( t - 1) (f) e - t H ( t - 2) (4) In this exercise, you will examine the effect of shifts in the time domain on the Laplace transform (graphically). (a) Sketch the graph of f ( t ) = sin t in the time domain. Find the Laplace transform F ( s ) = L{ f ( t ) } ( s ). Sketch the graph of F in the s -domain on the interval [0 , 2]. (b) Sketch the graph of g ( t ) = H ( t - 1) sin( t - 1) in the time domain. Find the Laplace transform G ( s ) = L{ g ( t )

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s11_mthsc208_hw14 - MthSc 208 Spring 2011(Differential...

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