Question

Q1- For the system shown below, with small mass of value (m) and lever of mass moment of inertia (J). • find equivalent mass, equivalent stiffness, and equivalent damping, all these interms of (x) displacement . Get equation of motion Interms of these equivalent quantities. • Find natural frequency (Wn) and damping ratio (zeta). • Find X(t) when the system condition is critically damping ,,X(0)=M and v(0)=0. tinfring

Answer 1

7 m ܠܓܥ f To o. angle is displaced by an rod Let the K(eo) one spoing (left) is so, compression other kle ) expansion CS Scanned with CamScanner

2 (a) so, writing frame the eq? of force balance for the keo keo Tex=caé O O + (cdo) a + (J + mf²) ö = (2K eo) e + Celė + (ke) e=0 so EI + mp3) mass So, equivalent J + mt? And ake2 Keg meg meg so keq = ake2 And 2 z wn = cd² It mf? cd² CS Scanzez kez Scannes +me It mf

so, cd² 3 २ Sake? (It mp 2) ( b ) cq of motion tory of eq quantities. (mea) ö + Cep) o + (keq) o=0 ( ) Natural wn) ver - frequency men 11 ake² I + mph Damping ratio (3) cd² les+mt) As mentioned past (a) za. (d) for critically damped system ö (23wn) (n) = CS Scanned with CamScanner So, + wn) • + + =0 و ہ (ن)

☺ x + Sog o= A + +BtJea [By differential calculmy] where Q= -z I 321 so, far 37 2 = -1 so; 0 = @ +6+) et Bet) — 6) + (A +8t) et (By differenticating mo)=M A so M V-O T so, o = A + B + O= (m-m+ So, CS Scanned with CamScanner