Take the Laplace transform of the IVP dy - y = -10 cos(kt), y(0) = -2 dt Use Y for the Laplace transform of y, (not Y(s)). So -10s Y: = === ☐ 8+0 and y(t) = + -2 82+k2 + s-1
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- Find the Fourier transform of A(t/4). (a) sinc2 (w/4) (b) sinc²(w/2) Sine (@, (c) sinc²(w) 2. (d) sinc²(2) (e) Maxing to another eu22/onwill s8ve this re one 2Type here to searchConsider f(x) = xe The Fourier Sine transform of f(x) F,f(2) = The Fourier Cosine transform of f(x) Felf)(2) = Note that while we usually denote the transformed variable by a the transformed variable in this case is 21.Q)find the inverse Laplace transform (3 L-' (P²t1) P-1 (4) L- 2P (P²-1)²
- Find the Fourier transform of sinc (2t). (a) 2n A(w/2) 3. (b) п Д(u/4) A(w/8 (d) A(w/16) Moving to the next ouestion.prevents changes to chis anaWerThe Fourier transform of 20 sinc (10(t - 2)) is 1. 2 rect (f/10) 2. rect (f/10) e14nf 3. 2 rect (f/10) ei4nf 4. 2 rect (f/10) e*j4rtfShow that d(w) ==}6(w − 1) +5(w+1)] is the Fourier transform of cos(t). - Show that d(w) = −ix[8(w − 1) − 8(w+1)] is the Fourier transform of sin(t).