Question

take the inverse laplace transform of x(s)=(1/(s^2+9))(15.25/(s^2+9.61))

Answer 1

x(s)=(1/(s^2+9))(15.25/(s^2+9.61))

x(s)=(15.25)/(s^2+9)(s^2+9.61), using partial fraction

(15.25)/(s^2+9)(s^2+9.61)=A/(s^2+9) + B(s^2+9.61)
15.25=A(s^2+9.61) + B(s^2+9)
15.25=A s^2 + 9.61A + B s^2 + 9B
15.25=9.61A +9B (1)
0= A + B, A=-B sub this in eq(1)
15.25=-9.61B +9B
15.25=-0.61B
B=-25 and A=25 therefore
X(s)=25/(s^2+9) -25(s^2+9.61)
L^1[X(s)]= (25/3)sin 3t -(25/3.1)sin 3.1 t

Answer 2

L^-1[X(s)]= (25/3)sin 3t -(25/3.1)sin 3.1 t

Answer 3

is this related to the differential equation we look at earlier? I know nothing about
L aplace transforms but the numbers are similar to the diff. question?

Answer 4

it seems they are similar...

Answer 5

X(s)=25/(s^2+9) -25/(s^2+9.61)
L^-1[X(s)]= (25/3)sin 3t -(25/3.1)sin 3.1 t but the wolfram answer is different....lol