1. Use the denition of Laplace Transform to nd the L.T. of the following functio

ID: 1810813 • Letter: 1

Question

1. Use the denition of Laplace Transform to nd the L.T. of the following function:

(a) g(t) = cos(wt)

2. Find the Laplace transform of the following functions:

,,,,,,,,,,,(a) f(t) = [t^2- 3t]u(t)

,,,,,,,,,,(b) cos(2t)u(t)

,,,,,,,,,,(c) sin(2t - pi )u(t)

,,,,,,,,,(d) sin(t)cos(t)u(t) Use Trig. Identity

,,,,,,,,,,(e) f(t) = t^2-e^-2t u(t) ; use first shifting theorem

3. Find the inverse Laplace Transform of the following functions:

,,,,,,,,,,,,a) s/(s^2+4)

,,,,,,,,,,B) s/(s+4)

,,,,,,,,,,,C) s-2/(s^2+4)

,,,,,,,,,,,D)10/(s^2+10)

,,,,,,,,,,,E)20/(s-1)(s+4) , Use partial fraction expansion

************shpw your work in paper plz*************

1. a) s/(s^2+w^2)

2. a) 2/s^3 - 3/s^2

b) s/(s^2 +4)

c)e^-pies(2/(s^2+4))

d)(1/2)(2/(s^2+4))

e) 2/s^3 -1/(s+2)

3.a) cos2tu(t)

b) del(t)- (4)e^-4t

c) (cos2t - sin2t)u(t)

d)root(10)sin(root10)tu(t)

e) (4e^t -4e^-4t)u(t)

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