Question

2) Use the Duhamel integral method to derive the expressions for the response of the undamped system subjected to the forcing functions shown in fig A. Set up the expression for x[t) in fig. B Ft 0.sto MA 2+ 0.5 € Fig A

Answer 1

Sorution!- The Duham e i rigral me tho d. Expressions tor th response of then undamped SYs lem fon etions from gren tijunes. freing fon etiong fom Subiected to the gren by hence he response of the Sys tem is unit Impuise response function the Condition of the the undamped Case th oni t impulse & the fonc tion for vesponse fonction : Th unit impuse response function tor the undamped Motion is Sin wt het) OLt< to force fune tion fet) To ts to Fo hence overall response is gun by ost c to fo Tsinio (t-T) dt to FO (wt- Sinwt- mwto

fs to =) x it) = 7 SIn WL f-T) d (Fo Sin wlt-T) to (1- cascult-to) (wto-Sinwlo) + mw? fo moto (cot-Sincot), The overall, response becomes fo muo fo - Sin wto) (1- Coso (1-to), {>to to x(4) = (2oto - mw?to