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)](https://www.tinkutara.com/question/Q198465.png)
$${The}\:{furier}\:{series}\:{approximation}\:{to}\: \\ $$$${the}\:{forcing}\:{function}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({t}\right)=\mathrm{5}\left[\mathrm{1}+\frac{\mathrm{4}}{\pi}\left(\frac{}{}\frac{{sin}\mathrm{120}\pi{t}}{\mathrm{1}}+\frac{{sin}\mathrm{360}\pi{t}}{\mathrm{2}}+\frac{{sin}\mathrm{600}\pi{t}}{\mathrm{3}}\right.\right. \\ $$$$\left.\:\left.\:\:\:\:\:+………\right)\right] \\ $$$${The}\:{transfer}\:{function}\:{for}\:{this} \\ $$$${problem}\:\:{T}\left({s}\right)=\frac{{X}\left({s}\right)}{{f}\left({s}\right)}=\frac{\mathrm{1}}{{ms}^{\mathrm{2}} +{cs}+{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{0}.\mathrm{001}{s}+\mathrm{1}} \\ $$$$\mathrm{1}.\:{plot}\:{the}\:{amplitude}\:{spectrum}\: \\ $$$$\mathrm{2}.{Obtain}\:{the}\:{expression}\:{for}\:{steady}\: \\ $$$$\:\:\:\:\:\:\:\:{displacement}\:{X}\left({t}\right) \\ $$
Commented by BHOOPENDRA last updated on 20/Oct/23
