12.40 Find f(t) for each of the following functions: b) f(s) - 1359 + 13432 +...
Find the inverse Laplace transform of each of the following functions. a. F(s) = 4652 + 4) f(t) = c++{F(s)}(€) = [" 58 b. G(s) = 7 (s – 5)2(52 +36) g(t) = £•*{F(0)}(€) = *
Find the inverse Laplace transform of each of the following functions. a. F(s) = 5 $4(s2 + 4) t f(t) = 2*4{F($)}(6) = dw b. G(s) = 4s (s + 5)2( 32 +81) g(t) = •{F()}(t) = dw
Find the Laplace transforms of the following functions: a) f(t) = sin(at + b) Using the integral of the Laplace transform b) f(t) = cos(t) + sin(t/2) You can directly use table 5.1 Tableau 5.1 Transformées de Laplace les plus couramment utilisées f(t)= £. {F()} F(s)= £{f(t)} f(t)=1 F(s) = 2 f(t)=1 F(s) == 2 3 Sl)=12 F(s) n! 4 St=1" F(s)=- 5 () at F(s)- S-a n! 6 S()=1"ar F($)= (s-a)"+1 a 7 s(t)= sin(at) F(s) s? +a? S...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...
7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1) 7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1)
Find the inverse Laplace transform, £^{F(s)}, of each of the following functions. Be sure to show all your worl 1. F(S) (s+2)3 = s+1 2. F(s) = $2 +48 $2 3. F(s) = (8-1)(8+1)(s+2) • 4. F(s) 6s+3 $4+592 +4 5. F(s) = 16 1 S 6. F(s) (s+2)(s2+4)
1.) 2.) Find f(t) for the function F(s) = 52 - 8s + 4 (s + 1)(8 + 2)2 Multiple Choice O =-24e-t+ + (-12)e-2t+6 +(-24)te-27 O 19 = (13e-++(-12)e-2t +(-24)te-210 O p0 = (13e-+ +(-24)e-2t+ (-12)te-24) (0) O 10 = 8e-t +(-12)e-2t *+ (-24)te-27 Identify f(t) for the function F (s) = 32 + 1 (s+3)(s2+4s+5) Multiple Choice 5e-3t_4e-2 tsin(t) О (5e-3t_4e-2tcos(f)( (5e-3t+4e-2tcos() 4e-36-5e-2tcos()
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)* sin(67) dt L{v(t)}(s) = b. g(t) = [ e 2-3(t-1) cos(71) dT L{$(t)}(s) = c. y(t) = e5(t-1) sin(97) cos(6(t – T)) dt L{s(t)}(s) =
10s - 15 (1 point) Consider the function F(s) 52 – 38 + 2 a. Find the partial fraction decomposition of F(s): 10s - 15 $2 – 38 + 2 b. Find the inverse Laplace transform of F($). f(t) = { '{F()} = help (formulas)
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...