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DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
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- Find the Fourier transform of the functions as:arrow_forwardObtain the Fourier transform of the function where f(x) = 0 for x < 0 and f(x) = e−axsin(bx) for x > 0.arrow_forwardUse Laplace transforms to find the equation of the current as a function of time i(t) in a series circuit with inductance L=0.1H, resistance R=452 capacitance C=2-10ʻF, and constant voltage V=12V if the initial current i(0)=0 and the initial charge q(0)=0. Recall that i'(0) = V – Ri(0) –arrow_forward
- Q1) Find the Laplace transform of the following functions:- f (t) = t e-3t sin²tarrow_forwardFind the convolution of f(t) = 3t and g(t) sin (2t). You can either calculate f * g directly, or approach it using the Laplace transform. =arrow_forwardWhat would the inverse Laplace Transform be for the attached function if A = 1+j4 and B = 3+j7? Please use cosines to replace complex exponentials and convert any phase angles to degrees.arrow_forward
- Describe in your own words the method you would use to find the Laplace transform of the first derivative, i.e., . From 2 examples.arrow_forwardIf F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = -eit f(t) may be expressed as G(w) = AF(w - b). %3D Enter A: Enter b:arrow_forwardA 4-pound weight stretches a spring 2 feet. The weight is released from rest 12 inches above the equilibrium position, and the resulting motion takes 7 place in a medium offering a damping force numerically equal to times the instantaneous velocity. Use the Laplace transform to find the equation of 8 motion x(t). (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) =arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage