(a) Find the inverse Laplace tmnsform of the function 3s2 I 2s + 2 Y(s) = (s + 2)(s2 + 2s + 5)'

by using a complete partial fmction e:~:pansion.

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(b) Find the inverse Laplace lmnsform of the same function by using the method of completing the sq·uare.

Problem :3.5

(a) Shov: that the following rotational rnechanical is repn:scnted by the diffeTential equation Negligible Jnenia Rotational Mechanical System

(b) Giccn the follou,inq infoTmation: w(t) = 10. b1 = b·2 = 0 and .J = 2 . . find T the time constant and wlss, thr stuuly slalr.

(c) Deduce !.hr response (solution to the equation).

(d) Solve the samt' differential equation in

(a) with the du.ia iu {b) by using Laplace tmnsforms.

(e) Plot the system response and (:onfirm your plot using the IVT and FVT.

Problem