f(t) = [5+ (4e2+ + 6te-2)e-24]u(t) A Find F(S) = L[f(t) as a proper rational function....
Show work by hand please. no matlab
1. Solve the following Laplace Transform problems: (a) (20 points) Given the following function f(t) = [10+ (4e-2+ + 3te-4t)e2t]u(t) A Find F(s) = C[f(t) as a proper rational function. F(8) must be in fully factored form. (b) (20 points) Let: f(t) = Ś(n + 2)!e=n(+36)(t – 3n) Find F(s) = [f(t) as a proper rational function.
Verify the following using MATLAB
2) (a) Consider the following function f(t)=e"" sinwt u (t (1) .... Write the formula for Laplace transform. L[f)]=F(6) F(6))e"d Where f(t is the function in time domain. F(s) is the function in frequency domain Apply Laplace transform to equation 1. Le sin cot u()]F(s) Consider, f() sin wtu(t). From the frequency shifting theorem, L(e"f()F(s+a) (2) Apply Laplace transform to f(t). F,(s)sin ot u (t)e" "dt Define the step function, u(t u(t)= 1 fort >0...
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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()
(16 points total) Let g(t) = (2-sin t)2, (a) (4 points) Find a rational function f(z) such that f(e)) 5. t (Hint: Let z = eit and express cost and sint in terms of z) b) (3 points) Find and classify all the isolated singularities of the function f(2) in part We were unable to transcribe this image
4. Describe how to find the possible rational zeros of a polynomial function. Use the function f(x)-2x +13-9x2 a. List all possible rational roots b. Use Descartes's Rule of Signs to determine the possible number of positive and negative f(x) = 2t to answer the following. real roots c. Use synthetic division to test the potential rational zeros and find an actual zero d. Use the quotient from part(c) to find all the remaining zeros e. Rewrite f(x) in completely...
Find the domain of the rational function f(x) = 24 OA) D(f) = {x | - 00 < x < -2 } OB) D(f) = {x 1 - 2 < x < 00 } OC) D(F) = {x | x # 2} D) D(F) = {x | x # +2} OE) D(f) = {x| - 00 < x < 2 } OF) D(f) = {x | x + –2} OG) D(f) = {x | 2 < x < 0 }
Consider the function f(t) whose Laplace transform F(s) = L{f(t)} = $5+2 We know f(0) = 0 and f'(0) = 4. Answer the following questions. Please write down the numerators and the denominators separately. Use "A" for the power operation, e.g., write s^5 for 5”. • L{f"(t)}= - Lle="r() = - 19(e) = 'ermite – wsin(26) dw, men zl940)= • If g(t) = wf(t – w)s in (2w) dw, then L{g(t)}= • If y(t) = L-'{e-35F(s)}, then y(1) =D and...
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)
Problem #24: Find the Laplace transform F(s) - {S0) of the function () = (2-1) [U(1 - 2) - Uit - 6)). [2 marks]
#6.) Given f(t)=-2:+8, Ost<4, f(t+4)= f(t). Find F(s)=L{f(t)} of the Periodic Function.