Find the Laplace transform of each of the following functions and simplify the result. Problem no. 7 only. Thanks! ExercisesFind the Laplace transform of each of the following functions and simplify the result.2aF(s) =1. f(t) = 2(1–e")s(S+a)(6s – 48)F(s) =s? +4s +402. f(t) = 2eª(3cos6t – 5sin6t)12F(s) =(s+4)*%3D3. f(t) = 2t'e"2e %F(s) =(s+3)%4. f(t) =Го4et-3)-3st<3G(s) =(s-1)5. g(t) =t23cos 2 t- t2seG(s) =(s² + 4)6. g(t) :4e 6*G(s) =t<5t257. g(t) = [(t-5)²(s-2)G(s) =(s- 2)² +1 (s-2)² + 49_(s-2)8. g(t) = 2e"sin4tsin3t3e% sin3tsinh 7t4.54.5H(s) =(s – 6.5)² +9 (s+7.5)² +9j2H(s) =s(s- 4)9. h(t) =10. h(t) = e"sinj2tProduct Identitiessin(A +B)+ sin(A –B)sinA cosB1.sin(A +B)- sin(A -B)cos A sinB2.cos(A -B)+ cos(A+B)cos A cosB:3.2cos(A -B)- cos(A+B)sinA sinB4. Table of Laplace and Inverse Laplace TransformsTime DomainComplex Frequency DomainF(s) = L f(t)Functionsf(t)Ø(t)H(t)Unit Impulse1Unit Step (Heaviside)1/se "/sVs?H(t-a)-asUnit Rampn!Polynomialsit4st12)pla-X (n=1,2..)(1)(3)(5)....(2n – 1)/ (-)2"1(s'k)Exponentialekth OrderExponentialn!t'e(s'k)""Sine Wavesin bts +bCosine Wavecos bts +bsinh bts -bcosh bt-b'Damped Sine Wavee" sinbt(s'k}° +b²Damped CosineWave(s`k)(s kỷ +b²" cosbtb' sinhbt(s k)' -b"(s`k)(s`k -b?e" coshbt2bst sin bt(s² +b² y°(s² –b²)(s² +b³ }°2b(s² +b° °t cos btsin bt – bt cosbt- 10 -1030

Answered: Image /qna-images/answer/c64f2e9e-ad71-412e-b2b9-57b33c4132a5.jpg

Answered: t<5 7. g(t) = |(t-5)² t25

t<5 7. g(t) = |(t-5)² t25

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A. Find the Laplace transform of each given expression, all letters except a, t, and 6 are constant. You may use the table. (1) t3 + 8(t-3)+ sin(wt) (2) + x +t sin (3t), where x= x(t), a function of time with initial conditions (0) = x(0) = 0
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Relate the concept of Laplace Transform to solve the following problems.
Determine £1¹{F}. L F(s) = 2 6s +80s +226 (s-3) (s² + 10s +26) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.