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## SEP291 Engineering Modelling-Matlab

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1. Obtain the Laplace transforms of the following functions:a. π‘π‘2ππ−2π‘π‘+ππ−π‘π‘cos(3π‘π‘)+5b. π‘π‘3−5cos (5π‘π‘)2. Find inverse Laplace transform of the following functiona. π π 2+π π +1(π π +1)(π π +2)2(π π 2+4π π +9)b. 2π π +1(π π −2)(π π +2)23. Using Laplace transform methods, solve for t≥0 the following differential equation,9ππ2π¦π¦πππ‘π‘2+12πππ πππ +4π¦π¦=ππ−2π‘π‘Subject to π¦π¦=1 and πππππππ =1 at t=04. Using the formulasβτ΅ππΜτ΅=π π β{ππ}−ππ(0) or βτ΅ππΜτ΅=π π 2β{ππ}−π π π  (0)−ππΜ(0)Find β{ππ}...

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#### Question Preview:

1. Obtain the Laplace transforms of the following functions:a. π‘π‘2ππβ2π‘π‘+ππβπ‘π‘cos(3π‘π‘)+5b. π‘π‘3β5cos (5π‘π‘)2. Find inverse Laplace transform of the following functiona. π π 2+π π +1(π π +1)(π π +2)2(π π 2+4π π +9)b. 2π π +1(π π β2)(π π +2)23. Using Laplace transform methods, solve for tβ₯0 the following differential equation,9ππ2π¦π¦πππ‘π‘2+12πππ πππ +4π¦π¦=ππβ2π‘π‘Subject to π¦π¦=1 and πππππππ =1 at t=04. Using the formulasβτ΅ππΜτ΅=π π β{ππ}βππ(0) or βτ΅ππΜτ΅=π π 2β{ππ}βπ π π  (0)βππΜ(0)Find β{ππ} when ππ(π‘π‘)=π‘π‘πππππ +cosh (π‘π‘), where k is a constant and βcosh(t)β is a hyperbolic cosine function.5. The following f(t) is a periodic function of period 2Ο defined over the period 0β€tβ€2Ο.Express f(t) as a Fourier series expansion.6. Find the Fourier series of the function f(x), of period p=2Lππ(π₯π₯)=τβ8 π€π€βππππβ2<π₯π₯<08 π€π€βππππ 0<π₯π₯<2, ππ=2

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