Mechanical engineering assignment

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Mechanical engineering1MECHANICAL ENGINEERINGBy NameCourseInstructorInstitutionLocationDate
Mechanical engineering2Question 2.A Fourier series approximation to the force show a sequence of approximations.Given P=231340561Let A= (v1, v2, v3)By the given conditionsPu1= v1Pu2= v2Pu3= v3That is matrix equation PA= V = (v1v2v3)PA=VP-1PA = P-1VA= P-1VNow|P|=-1 and adjoint (p) =432973431^ TThen P-1=494323213Therefore A = P-1V =494323213368462545=444663436511105
Mechanical engineering3U1=443411U2=463610U3=655Question 3.The amplitude is given by:A=Fo/s(1¿(wwn)n+(23wwn)2)¿Wn=s/m =3000/6=105A=80/3000¿¿¿=80/3000¿¿¿=0.023668mTherefore A= 2.3668cmWhere by FO=80Nf=8cpsrs =3000N/mw=2πf
Mechanical engineering4m= 6kgBut=0Then y =Asin(wt+)Note:is the phase difference (not given)QUESTION 4By Duhamel's method the response of the system is given by the convolution of the unitimpulse response function and the forcing function. For the undamped case, the unit impulseresponse function is:The unit impulse response function for the undamped motion is:The forcing function is given by:The overall response is thus given by:
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