Find f(t). f(t)= -3t^2 e^-t -7te^-t -t+8 -8e^-t...? 5x-1 Find fit). L'{ x2(x+1) f(x)=? Use Laplace.
Find Laplace Transform for the following functions: 5- f(t) = 3t^e2t 6- f(t) = e-+(2+* + 3t2 +10) 7- f(t) = e-4 cos(3) Find Laplace inverse: 5- F(s) 2 2+9 6- F(S) = (s+3)* 7- F($) = (s+1)(8-2) 10 8- F(s) = (3-3)(s+4) 9. F(S) s(s-1)(3-4) 35+1
dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)", (a) [t3e-36] (b) C[(t + 2)2e'] (c) C[t(3 sin 2t - 2 cos 2t)] (d) L[tsin t] (e) C[t cosh 3t) (1) [(t-1)(t - 2) sin 3t] (g) [t3 cost] 9. Applying L[t"f(t)] = (-1)", , calculate (a) Sºte-3t sin t dt (b) Scºt?e-t cost dt recimento e contato Llegarsim 225 (-1)" IEC d'Fs) dsh
1. Find the Laplace transform of the function f(t) = 1 + 2t + 3e-3t - 5 sin(4t). Solution: 2. Find the inverse Laplace transform of F(s) = 7+ (8 + 4)(18 - 3s) (s - 3)(s – 1)(s + 4)" Solution:
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet
Find the Laplace transform of f (x) = 2 e−3x + cos 2x + 5x.
2t +1 if 0 <t< 2 Consider f(t) = { | 3t if t > 2. (a) Use the table of Laplace transforms directly to find the Laplace transform of f. (b) Express f in terms of the unit step function, then use Theorem 6.3.1 to find the Laplace transform of f.
QUESTION 3 After use Laplace Transform to transform the following initial value problem X" +x=e-t, x(0) = 1,x'(0) = 1, S-2 you should get X(s)= (write fraction as (S-2)/(5-4)(8+6) for -). Then, find (s-4)(8+6) x(t)= L-?{X(s)}= (write 5/6 by 5 -30 6' e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
Use Laplace transform definition to find L{f(t)} f(t) = e-4t cost
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Find the Laplace transform of the function f(t). f(t) = sin 3t if 0 <t< < 41; f(t) = 0 ift> 41 5) Click the icon to view a short table of Laplace transforms. F(s) = 0