s-1 s(s+ 1)² -1+et+2te-t 2+te-t-e-t O Option 1 Option 3 1+et-2te-t Option 2 -2+tet + et O Option 4

Q: se-2s c) F(s) (3s+4)(s-1)

A:

Q: 7.2 . 2 S 1 s – 2

A:

Q: F (s) = e4-3s (s+4)5/2

A:

Q: 6s L-1 (s² + 9)²

A: Apply the inverse transform rule that is if L-1Fs=ft  then L-1sFs=ddtft+f0  . The expression 6ss2+92…

Q: 3(s-4)e-5s F(s): %3D s2-8s+25

A:

Q: Evaluate t=0.01, Given: 21' + 20I = 100sin(150t) Round-off to 3 decimal places.

A: Given differential equation is2I'+20I=100sin150tI is evaluated at t=0.01 as shown below.

Q: 3s2 + 5s + 1 (s)= (s2 + 15s + 34) %3D

A:

Q: 23. F(s) = 5s² + 34s + 53 (s+3)²(s+1)

A: We will partial fraction decomposition to separate the factors of denominator and then use inverse…

Q: y! ty =e*t which catis fies the conditions y (0 %3D

A:

Q: f(1) = sin? (t + x) sin (t + ) = S1

A: Given:      ft=sin2t+π

Q: Solve for the Inverse Laplace of this equation

A:

Q: d²x 2. dt dx dx 2- + 3x = 0 x(0) = 1, (0) = 0 - dt2 dt

A:

Q: 3s +2 1 Find L-1 s2 + 4s + 29

A: To find laplace inverse.

Q: f(S) 7 (S+2) (S+2)(s2-4S+20) QI/ A)Find the inverse of elue

A:

Q: d²x dx dx -(1) = 2 4- + 4x = 0 x(1) = 0, - dt2 dt

A:

Q: 1) S-4 5²-85+ 10

A:

Q: L[(t-$)°u(t-)+(tt) sinh (t-Đ]

A:

Q: Examples: find the inverse laplace F(s) = 2s2 + 5 s3 +6s? + 5s -12

A:

Q: 6 F(s) (s? –48+20)? cos 4t 3 -2t sin 4t 3 -2t O f (t) te 64 16 t e2t cos 4t 3 2t sin 4t 3 O f (t) 64…

A: Inverse Laplace property

Q: S-a (s-a)'tb2

A: Inverse Laplace transferom

Q: ₂ (91+₂²) - F(S)

A: Given: Fs=1s2+162. We have to find the inverse Laplace using convolution.

Q: I- 100 (s+10) (s+20)

A: Inverse Laplace transform

Q: 13. e-2t cosh³ 2t 14. cosh at cos at V3 t 15. sinh sin: 2

A:

Q: answer this inverse laplace

A: Apply Laplace inverse on both sides

Q: 10 [s(s+4)(s+5)²

A: