#4 (50 pts) Apply related theorems and tables to find the Laplace transform. sin cos(1 –...
#3 (50 pts) Use the Laplace transform (including all tables and theorems) to solve the initial value problem. y"- 4 y'= 6e" – 3e", y(0) = 1, y '(0)=-1
#2 (50 pts) Find the inverse Laplace transform of the following function by using Theorems and tables 2s +5 $? +68 +34)
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of f(t) = (cos(2t) + e-4t)-u(t) (simplify into one ratio)
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of 3s 7 82 -2s + 10 (b) Hence determine the inverse Laplace transform of 3s +7 -2s S2-2s10
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of 3s 7 82 -2s + 10 (b) Hence determine the inverse Laplace transform of 3s +7 -2s S2-2s10
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of s +3 82 6s 16 (b) Hence deduce the inverse Laplace transform of 83 -6s e s2 6s 16
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of s +3 82 6s 16 (b) Hence deduce the inverse Laplace transform of 83 -6s e s2 6s 16
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
6. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e sin (2(t5) H(t5) (b) Hence, find the Fourier transform of 6 e-3t-it sin (2(t +5)) H(t+5).
6. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e sin (2(t5) H(t5) (b) Hence, find the Fourier transform of 6 e-3t-it sin (2(t +5)) H(t+5).
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform 2. tan" G) 3. Check the existence of the Laplace transform for the given function and hence she that -02:49 in 133+ 4 S- where LF(t)) is represent the place transform of (1) [Hint: 2 cos Acos B = (A-2).sin(A+B) + sin(A - m = sin cos sin(A + B) - Sin(A) = 0 4. Find the Fourier Sine series of f(x) <rci 5....
Find the Laplace transform F(s) L(f(t)) given f(t) = 5e-4 sin(5t) + 2e cos(6t). F(8) =
Find the following Inverse Laplace transformations. Use the
Laplace Transform table attached in the next page. Show all your
work, how to get partial fractions etc. and clearly state the
Laplace rule(s) that you used in the related step from the attached
Laplace Table. (?) ℒ −1 { ? 2−?+2 ?(?−3)(?+2) } (?) ℒ −1 { ? −? ? ?
} (?) ℒ −1 { 1 ? 2−2?+1 }.
Q1. (15 pts) Find the following Laplace transformations. Use the Laplace...