LAPLACE/ Simple Fourier / Simple Z table

Question 1

LAPLACE TRANSFORM OF:

1

Answer 1

1 / s

Question 2

LAPLACE TRANSFORM OF:

t^n

Answer 2

n! / ( s^[n+1] )

Question 3

LAPLACE TRANSFORM OF:

√ t

Answer 3

(√π) / (2*s^0.5 )

Question 4

LAPLACE TRANSFORM OF:

e^at

Answer 4

1 / (s - a)

SHIFTING THEOREM

Question 5

LAPLACE TRANSFORM OF:

sin (at)

Answer 5

a / (s² + a²)

Question 6

LAPLACE TRANSFORM OF:

cos (at)

Answer 6

s / (s² + a²)

Question 7

LAPLACE TRANSFORM OF:

t*sin (at)

Answer 7

2as / (s² + a²)²

Question 8

LAPLACE TRANSFORM OF:

t*cos (at)

Answer 8

(s² - a²) / (s² + a²)²

Question 9

LAPLACE TRANSFORM OF:

sin (at + b)

Answer 9

[ssin(b) + acos(b)] / (s² + a²)

Question 10

LAPLACE TRANSFORM OF:

cos (at + b)

Answer 10

[scos(b) - asin(b)] / (s² + a²)

Question 11

LAPLACE TRANSFORM OF:

sinh (at)

Answer 11

a / (s² - a²)

Question 12

LAPLACE TRANSFORM OF:

cosh (at)

Answer 12

s / (s² - a²)

Question 13

LAPLACE TRANSFORM OF:

e^at) * sin (ωt

Answer 13

ω / ((s - a)² + ω²)

Question 14

LAPLACE TRANSFORM OF:

e^at) * cos (ωt

Answer 14

(s - a) / ((s - a)² + ω²)

Question 15

LAPLACE TRANSFORM OF:

e^at) * sinh (ωt

Answer 15

ω / ((s - a)² -ω²)

Question 16

LAPLACE TRANSFORM OF:

e^at) * cosh (ωt

Answer 16

(s - a) / ((s - a)² - ω²)

Question 17

LAPLACE TRANSFORM OF:

t^n ) * (e^at

Answer 17

n! / ( {s - a}^[n+1] )

Question 18

LAPLACE TRANSFORM OF:

UNIT STEP
u(t - c)

Answer 18

[ e^(-cs) ] / s

Question 19

LAPLACE TRANSFORM OF:

DIRAC DELTA
δ(t - c)

Answer 19

e^(-cs)

Question 20

LAPLACE TRANSFORM OF:

f’(t)

Answer 20

s*F(s) - f(0)

Question 21

LAPLACE TRANSFORM OF:

f’‘(t)

Answer 21

(s² * F(s)) - (s * f(0)) - (f’(0))

Question 22

LAPLACE TRANSFORM OF:

∫ f(t) dt

Answer 22

F(s) / s

Question 23

LAPLACE TRANSFORM OF:

f(t - a)

Answer 23

if laplace of f(t) is F(s),

Laplace of f(t - a)
e^(-a*s) * F(s)

TIME SHIFTING

Question 24

Z TRANSFORM OF:

DIRAC DELTA
δ(n)

Answer 24

1

Question 25

Z TRANSFORM OF:

UNIT STEP
u(n)

Answer 25

z / (z - 1)

Question 26

Z TRANSFORM OF:

b^n

Answer 26

z / (z - b)

Question 27

Z TRANSFORM OF:

n

Answer 27

z / (z - 1)²

Question 28

FOURIER TRANSFORM OF:

DIRAC DELTA
δ(t)

Answer 28

1

Question 29

FOURIER TRANSFORM OF:

DIRAC DELTA
δ(t - c)

Answer 29

e^(-iω*c)