F1 (s) = and F2 (S) = find the inverse Laplace transform of F(s) = F1 (s) F s+2 s+3' lote: the letter 's' does not clearly appear on the equation. [e-2t + e-3*]u(t) [e2t – e3t]u(t) [e-2t – e-3*]u(t)
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- the inverse laplace transform for the following function: X(s) = (5s + 2)/( s2 + (5/2)s + 1 ) i need detailed steps on how to complete the inverse transform of the above problem. if you could also include notes on how to procede on future problems will be greatly appreciated.Problem 5. Which gives the Laplace transforms of the given time-domain function? ln [(s + sqrt 2)/(s - sqrt 5)] ln [(s - sqrt 2)/(s + sqrt 5)] ln [(s - 2)/(s + 5)] ln [(s - sqrt 2)(s + sqrt 5)]let Vc (0-) = 2v in the circuit shown in the figure. Write an appropriate differential equation apply the Laplace transform on both sides and find Vc (t) if Vs (t) is equal to: a) 9u (t) V b) 9 cos tu (t) c) 9 e-t u (t) V
- Find the Laplace Transform of the following functions 2ws Ans. F(s)= 2) f(t)=tsin(wt) R ) 8 f©)=tsinh@n) Ans. FO=G )A 6 H inductor and a 30Ω resistor are connected in series with avoltage source of 10??? 20?. Use Laplace transforms as a function of time ifthe initial current is zero.. What is the current when ? = 2 ?solve for the laplace transform of D3y(t) + 5D2y(t) + 7Dy(t) + 3y(t) = 2+t where: y(0) = 0 Dy(0) = 0 D2y(0) = 0 Show complete solution
- Q3) a Find laplace transform of X (t)= et sin 2t for t ≤ 0 also indicate R.O.C please solve step by step subject signal and systemsFind the inverse Laplace Transform of H(s) = (8/(3(s2)+12)+ + 7/s5 COMPLETE SOLUTIONThe Laplace Transform can be used to solve differential equations using a four step process. 1.Take the Laplace Transform of the differential equation using the derivative property (and, perhaps, others) as necessary.2.Put initial conditions into the resulting equation.3.Solve for the output variable.4.Get result from Laplace Transform tables which in the picture. If the result is in a form that is not in the tables, you'll need to use the Inverse Laplace Transform. Solve the following DE using Laplace Transform Method:1. f(x) = e-2x (1-2x)
- The Laplace Transform of (t-4)u(t-3) is: Select one: a. e^(-3s)/s- e^(-3s)/s^2 b. e^(-3s)/(s^2+s) c. e^(-3s)/(s^2-s) d. e^(-3s)/s^2 - e^(-3s)/s e. e^(-3s)/s^2 + e^(-3s)/s Clear my choiceSuppose for the circuit shown, Idc=24 mA, R=625 Ω, L=25 mH, and C=25 nF. There is no energy stored in the circuit when the switch opens at t=0. 1. Find V(s), the Laplace transform of v(t). 2. Find v(t) by finding the inverse transform of the partial fraction expansion of V(s).1. (a) find laplace transform f(t) = 2u(t+1) sin2t + e2t δ(t+3) (c) find inverse laplace transform using convolution theorem L-1{4(s-1)/ s((s-1)2 +4)}