Question B1 (10 marks) (a) Show that the Laplace transform of the Heaviside function (or unit step function, u), with un

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Question B1 10 Marks A Show That The Laplace Transform Of The Heaviside Function Or Unit Step Function U With Un 1 (75.82 KiB) Viewed 24 times

Question B1 (10 marks) (a) Show that the Laplace transform of the Heaviside function (or unit step function, u), with unit step applied at t = a, is given by: L{u(t - a)} (2 marks) -as = S (b) Solve the following second order ODE with given initial conditions, by using the Laplace transform (8 represents the Dirac delta function): day dy +4 + 8y = e3t+48(t-5), y(0) = 0, y'(0) = 1 dt dt2 (8 marks) Hints - table of Laplace transforms: f(1) LIF) f(1) L(F) S 1 1 1/s 7 COS W1 $2 + m 2 w 2 1 1/s2 8 co sin wt من + 2ی 3 2 29/53 9 cosh at n! a 4 10 sinh at (n = 0, 1, ...) SNT S-a 5 ra (a positive) T(a + 1) fa+1 11 eat cos wt (s - a)2 + w2 1 6 eat 31- 12 eat sin wt S-a (s - a)2 + w2