Solve the following wave equation using partial Laplace transform: a²ua²u + sinxx; 0≤x≤ 1, tz0 at² ex² u(x,0) = 0,2(x,0) = 0 at u(0, t) = 0, u(1, t) = 0
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- A) Determine the Fourier Transform of the rectangular pulse signal II(t) = (1. - Sis 1, = 2 0, otherwisefind the laplace transform of the equations: a.) f(t)=2e^-2t (3cos6t-5sin6t) b.) f(t)= 2e^2t sin4t sin3tFind the approximation for the Green's function of the one-dimensional acoustic wave equation in the case where velocity is given by: c(x) = aebx , where a and b are real numbers and a > 0. Analyze each case, b 0, in detail.
- Solve for the Laplace transform of et sint cost cos 2t cos 4t +4s+20 4s+20 -4s+68 2-4s+8Find the laplace transform of f(t) = t e^2t sin(3t)Find the Fourier transform of the rectangular pulse: f(t) = 1 -T≤t≤T 2 dn = = FR sin utta da sin "* dx и Пх + ! cos nx T du (-Coy₁ WX -coga 0 ->|t| > T = -con 。) -T T ever
- Q1) a) Find the Laplace transform of: f (t)= est. cos² (3t) Find the Laplace transform of: f(t)= est. sin³(3t) B)Compute the inverse Laplace transform: -6 = u(t-c)(t-4)(-2e^(t-4)+2e^(-2(t-4)) e s2 + s – 2 (Notation: write u(t-c) for the Heaviside step function uc(t) with step at t = c.)b) Show that the ode (x + tan-¹ y) dx + x+y 1+y² dy = 0 is exact, then find the general solution and particular solution if the point (0,0), belongs to the solution. c\ Determine the Laplace transform of the function f(t) = (t + 2)².