Compute the Laplace transforms of the following functions: (a) f(t) = 2tt² + sin(t) − 5 (b) f(t) = (t+1)³ (c) f(t) = (t² (d) f(t) = { 1)u(t − 3) t for 0
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- Consider the function f(t) given by J1 if l비 <1 f(t) = |0 otherwise %3D Find the Fourier transform of f(t). Hence Find the Fourier transform of (i) f(t – 1) (ii) f(t – 1) cos 3t (iii) f(t – 1) sin 3t1. Find the Fourier transform of (a) f (x) = exp (-a.x²), (b) f (x) = exp (-a|x|), where a is a constant.3) Given that f(t)= 4 e-3(t-4) a) Find Adf(t)/dt] by differentiating f(t) and then using the Laplace transform tables in lecture notes. b) Find Adf(t)/dt] using the theorem for differentiation c) Repeat a) and b) for the case that f(t)= 4 e-3(t-4) u(t-4)
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