Question

9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b) The displacement of a particular mechanical system is governed by the following ordinary differential equation dy 10y f(t) 7 dt where y(t) is the displacement and f(t) is the applied load Page 2 of 4 MATH2124 SaMplE EXAM IV i Use the Fourier transform to obtain the impulse response h(t) of the mechanical system (ii) If the applied load is f(t) = H (t1)- H(t 1) (where H(t) is the Heaviside unit step function), write down the solution y(t) a convolution integral as

Answer 1

Ans:- Given that The inveyse Fouier ansfoim of the follouoing -fonction is w(5+) the Partial fraction Вiy applying A t C84) ca tiw)(5t) 5 iu) 1 = A (5+iu) B(ai then Put w5 -V3 A =a then NOw Чз 3 Cw(5) -hen taking inverse Fouriei txansfoym Ht) St -at - e

dy Given dy d& 10 y f(t) where yt) is the displacement (t is the applied load. Taking loplace tYansform on both sides teO Y(s)1 Y (s)s) Ys) S) S2S+10 (S+5(S+8) then ht)=% load is applied f(t) then the solution is h(t) is A)HCu)(H(t-*i) H (Lu-i) _4u -au 3e