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1. (a) Suppose the unit step function uc(t) has a generalized derivative u(t) everywhere. Find L[u'(t)]...
Please include step-by-step solution. D19. Solve t2x" +3tx -3 x-t', t>0.
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Find i(t) for t> 0 in the op amp circuit of Fig. P4. (u(t) is unit step function. It is 1 for t> 0 and 0 for t<0.) 1/6F It 3 Ω 212 + 2 u(t) V 1/6 F 10 Ω Figure P4
Determine Laplace Transform of f(t) = u(t – 2)u(t – 3). [hint: L[u(t)] => e3s 2s e38 e-35 s e-35 2s
7. (5 marks) Consider a smooth function u(x, y) satisfying: Urx + Uyy + Uzy > 0 in 12. . Show that u atains its maximum on the month ago Show that u attains its maximum on the boundary an.
2. Spts) Express (0) in terms of the unit step function ue(t) and find its Laplace transform. f(t) = 0, 0 St<1 2, 13t<4 Ten, t24
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
pls answer! my last attempt :) Use the step-by-step method to find io(t) for t> 0 in the circuit in the figure below. 36 V 4 k2 4 k2 24 ko X . 341 500uF t = 0 34 22 i.lt) Please round all numbers to 3 significant digits. Click here to enter or edit your answer jo(t) = mA Use the step-by-step method to find io(t) for t > 0 in the circuit in the figure below. 200 uF...
For the circuit represented in Fig. 9.54,(a) obtain an expression for uC(t) valid for all t> 0. (b) Determine uC at t 10 ms and t 600 ms. (c) Verily your answers to part (b) with an appropriate PSpice simulation. 1? 0.01 H I-0 5? FIGURE 9.54
PROBLEM 4. Determine the function u = u(t, x) if Ut = Uzz, t> 0, x € (0, 7), and u(0, x) = cos (x), uz(t, 0) = uz(t, 7) = 0.