Find the inverse Laplace transform of the transfer function Q-5 s+1 S+1 25 pts. s3 +2s2+9s+18(s+2)(s2+9)
9s 11 (1 pt) Find the inverse Laplace transform f(t) = L=1 {F(s)}| of the function F(s) s2 2s5 9s 11 f(t)= L' help (formulas) $2-2S+5
Question 1: [25 pts] S+1 a) Find the inverse Laplace transform of the expression $2+4 b) Find the inverse Laplace transform of the expression (s-5)(s2+4) c) Use the information from the parts a) and b) to find the solution of the IVP y" + 4y = 6e5t, y(0) = 1, y'(0) = 1.
3. Given the function s) = 2s2 + 2s + 1 (a) Find the inverse Laplace transform analytically, BY HAND CALCULATIONS
Use the convolution theorem to find the inverse Laplace transform of the given function s3 (²+1) 2 S? + 1)
(1 point) Find the inverse Laplace transform f(t) = --!{F(s)} of the function 5 9 F(s) = + 52 S+9 S 5 f() = 2-1 { + 640] = s2 help (formulas)
Find Laplace transform of ?(?) = 2 + 5? Find Laplace transform of ?(?) = 2?-t + 3??-4t Find time function corresponding to this Laplace transform: ?(?) = (2s2+s+1)/(s3-1) Solve this ODE using Laplace transform : ?̈(?)+2?̇(?)+4?(?)=0; ?(0)=1, ?̇(0)=2 Solve this ODE using the Laplace transform : ?̈(?)−2?̇(?)+3?(?)=0; ?(0)=2, ?̇(0)=1
Problem 5. Determine the inverse Laplace transform of Problem 6. Determine the inverse Laplace transform of 2s2 4s 10 9(s) = 2(s+1) Problem 7. Determine the inverse Laplace transform of 2s 10
5. Find the inverse Laplace transform of H(s) = 5s? +21s +18 (s +1)(s+2)?
Use the convolution theorem to find the inverse Laplace transform of the given function. 2 s(s? +1) 2 3 (s2 +1)
Use the convolution theorem to find the inverse Laplace transform of the given function. 2 $3 (s2+4) 2 >(t)= (s2+4) s3