
![= patste fut = [-este ] 3-e3tét + €3+ e test 23+ (1-ét) MORE 22445 - Eht Ca 4+ + Sin Ja 43 1. We know that Laplace bansform](http://img.homeworklib.com/questions/2464e190-0c45-11ec-8946-fd11722290f4.png?x-oss-process=image/resize,w_560)
8. (i) Find C[F(t)], where F(t) = { if 0 st 34, ift> 4 (ii) Compute...
Find the Laplace transform of the function f(t). f(t) = sint if 0 St< $41; f(t) = 0 ift> 41 Click the icon to view a short table of Laplace transforms. F(s)=
(1 point) Let Solve the differential equation using Laplace transforms. t/16-sin(4t)/64+3/4sin(4t)+4cos(4t) ft 4T y(t) = ift>4 -cos(4t)/16+1/16+3/4sin(4t)+4cos(4t)
Question 1 4 pts Find the Laplace transform of ift <TI, f(t) {i = 0 t-a if <t < 27 0 ift > 27 -TS e TS - -27s 1 s2 $ 1 eans 1 Te27 1 s2 (e-ws e=278) -TTS -27s 1 Te-27 1 s2 s O None of the above
QUESTION 9 Find the Laplace Transform of f(t)= - 1 ifts 4: f(t)=1 ift> 4.
Engineering Analysis
Q.1. f(t) = {S; if - 4 <t<o if 0 st <4 a) Sketch the function for 3 cycles [5 points ] b) Find the Fourier series for the function. [15 points)
2. If C is the space curve given by F(t) = (t, t”, t') (0 St < 1) and F(x, y, z) = (1+z, cos(TX), e24), find ScF. dr.
Find the Laplace transform F(s) - {0} of the function: f(t) = 1-21 0314 2-34 4 <t<6 14 6 by splitting the integral into three pieces. Enter your answers in order of increasing domain.
(a) Given the following signals: z(t) = { ={ex? exp(-kt) t> 0 0 t<0 sin(Ot) g(t) = **(t) art (i) Explain what the symbol * means in this context and write down the expression for the function y(t). (ii) Compute the energy of the signal x(t) in the time domain. (iii) Using the formulae 1 F[2(t)]() = k + 2ris F(II(t)](s) = sinc(s) It > 1/2 II(t) It < 1/2 sin(TTS) sinc(s) ITS compute the energy of the signal y(t)...
3. Find the Laplace transform off, where f(t) = 3 + 2 if Ost <3, f(t) = 0 if 3 st < 6 and f is periodic with period 6. 4. Solve y" - 16y = 40e4t y(0) = 5, y(0) = 9 using the Laplace transform.
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3. Solve come to 4. Solve C[f(t)) Where f(t) = 2t Osts 1 f(t) = t t > 1