QUESTION 10 Find the Laplace Transform of f(t) = 0 ift<1: f(t) = tiflsts 2: f(t) = 0 ift> 2. ign 5
Let α σ(t) with σ(t) = VG + and σο > 0. (i) Determine α such that for all t > 0 it follows Jooo dr |ψ(t,x)12-1. Remark: dyeV
Question 1 4 pts Find the Laplace transform of ift <TI, f(t) {i = 0 t-a if <t < 27 0 ift > 27 -TS e TS - -27s 1 s2 $ 1 eans 1 Te27 1 s2 (e-ws e=278) -TTS -27s 1 Te-27 1 s2 s O None of the above
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for any a, 0 < a < 1. b. Does {f,) converge uniformly on [0, 1]?
4. (10 points) A damped wave train is expressed by f(t) = Ae-iwot when t2t> 0; and f(t) = 0 ortherwise. a) Please find the power spectrum of this light; b) Please plot and discuss the spectrum when to = 5
Express the real part of the following signal in the form Ae-at cos(wt + ?) where a, co and ? are real and-? < ? 2. ? b. x(t) = je(4+/100)t L or a nower signal. Then
Real Analysis question, give clear writing please Let h(x) be the function on (0, 1) defined by ſi x <1 h(x) = 2 X=1 (a) For any P, what is the value of L(f,P)? (b) Can you find a P such that U(f,P) is within 1/10 of L(f,P)? (c) Show that h is integrable.
Find the Laplace Transform of f(t)=0 if t<1: f(t) = t if 13t<2; f(t) = 0 ift> 2.
(1 point) Let Solve the differential equation using Laplace transforms. t/16-sin(4t)/64+3/4sin(4t)+4cos(4t) ft 4T y(t) = ift>4 -cos(4t)/16+1/16+3/4sin(4t)+4cos(4t)
What is the value of i(t) for t>=0? Given L = 10 H, R = 5 ohms and Vs = 40V. URO - w vs 40e^(-0.5t) 20e^(-0.5t) 40e^(-0.02t) 8e^(-0.5t)