Please help me to solve just these questions a the second term is found from For

Question

Please help me to solve just these questions a the second term is found from Formula 9 using a Exercises 12.5 1. Derive the Laplace transform for f() t 2. Derive the Laplace transform for f t) cos Using Table 122. find the Laplace transform of each function f). sin 3t 6. f() 1 cos 7t 9. f(r) sin 2 cost 13. f() t sin 4t 14. f(r) 6r sin 6r 15. f(t) cos 5t 18, f() rsin 4r 1cos 4t Express the Laplace transform of each expression with the given conditions in terms of and 20. y" 2y: y(0) 0 and y' (0) 0 22. y 2y; y (0) -1 and y' (0) 2 23 3y" y: y(0) 1 and y' (0) 0 27. y" 6y y(0) 3 and y' (0) 7 28. y" 2y 3y; y (o) 4 and y (0) 5 6 and y'(0) 2 5 and y'(0) 30. y" 3y 2y; y (0) Using Table 12.2 find the inverse transform of each function F(s). 31, F(s) 33, F (s) 35, F() si 64 F(s) F() 40, F() 41. F() 42, F() 44, F(e) 45, F() 22s 38 47. F() 49, Show: R 12

Explanation / Answer

1) f(t) = t

L(t^n) = n!/(s^(n+1)

here n = 1 ,

hence

L(t) = 1/s^2

3) f(t) = sin(3t)

L(sin (at)) = a/(s^2+a^2)

here a = 3

hence 3/(s^2 +9)

7)

L(t^n) = n!/(s^(n+1)

here n = 2 ,

hence

L(t) = 2/s^3

Please ask rest question again

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