Lapace transforms

Question 1

f(t-T)u(t-T)

Answer 1

e^(-Ts) F(s)

Question 2

f(at)

Answer 2

1/a F(s/a)

Question 3

e^(-at) f(t)

Answer 3

F(s+a)

Question 4

f’=df/dt

Answer 4

sF(s)-f(0-)

Question 5

f”=d^2f/d^2t

Answer 5

s^2F(s)-sf(0-)-f’(0-)

Question 6

integral[0- to t] (f(~)d~

Answer 6

1/s F(s)

Question 7

t f(t)

Answer 7

-d/ds F(s)

Question 8

f(t)/t

Answer 8

integral[s to infi] F(s’) ds’

Question 9

delta(t)

Answer 9

1

Question 10

1 or u(t)

Answer 10

1/s

Question 11

u(t-T)

Answer 11

e^(-Ts)/s

Question 12

e^(-at) u(t)

Answer 12

1/(s+a)

Question 13

e^(-a(t-T) u(t-T)

Answer 13

e^(-Ts)/(s+a)

Question 14

te^(-at) u(t)

Answer 14

1/(s+a)^2

Question 15

t ^(n-1) e^(-at) (u(t)

Answer 15

(n-1)!/(s+a)^n

Question 16

sin(wt+theta) u(t)

Answer 16

(s sin(theta)+wcos(theta)) /(s^2+w^2)

Question 17

cos(wt+theta)

Answer 17

(s cos(theta) - wsin(theta)) /(s^2+w^2)