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The-furier-series-approximation-to-the-forcing-function-is-given-by-f-t-5-1-4-pi-sin120pit-1-sin360pit-2-sin600pit-3-The-transfer-function-for-this-problem-T-s-X




Question Number 198465 by BHOOPENDRA last updated on 20/Oct/23
The furier series approximation to   the forcing function is given by   f(t)=5[1+(4/π)((/)((sin120πt)/1)+((sin360πt)/2)+((sin600πt)/3)        +.........)]  The transfer function for this  problem  T(s)=((X(s))/(f(s)))=(1/(ms^2 +cs+k))                   =(1/(0.001s+1))  1. plot the amplitude spectrum   2.Obtain the expression for steady           displacement X(t)
$${The}\:{furier}\:{series}\:{approximation}\:{to}\: \\ $$$${the}\:{forcing}\:{function}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({t}\right)=\mathrm{5}\left[\mathrm{1}+\frac{\mathrm{4}}{\pi}\left(\frac{}{}\frac{{sin}\mathrm{120}\pi{t}}{\mathrm{1}}+\frac{{sin}\mathrm{360}\pi{t}}{\mathrm{2}}+\frac{{sin}\mathrm{600}\pi{t}}{\mathrm{3}}\right.\right. \\ $$$$\left.\:\left.\:\:\:\:\:+………\right)\right] \\ $$$${The}\:{transfer}\:{function}\:{for}\:{this} \\ $$$${problem}\:\:{T}\left({s}\right)=\frac{{X}\left({s}\right)}{{f}\left({s}\right)}=\frac{\mathrm{1}}{{ms}^{\mathrm{2}} +{cs}+{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{0}.\mathrm{001}{s}+\mathrm{1}} \\ $$$$\mathrm{1}.\:{plot}\:{the}\:{amplitude}\:{spectrum}\: \\ $$$$\mathrm{2}.{Obtain}\:{the}\:{expression}\:{for}\:{steady}\: \\ $$$$\:\:\:\:\:\:\:\:{displacement}\:{X}\left({t}\right) \\ $$
Commented by BHOOPENDRA last updated on 20/Oct/23

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