Question

Mech 411 (Sec 03) Quiz I Time Allowed: 20 min Sept 16, 2019 Your Name: Question: For the system shown with the connecting rod of mass m: 21/3 L/3 bar with mass m C Figure 1: Vibrating System (a) Find the equation of motion in 0 coordinate (rotation around point O) (b) Find meg and keg (c) Find the natural frequency Assume that system starts oscillating from the equilibrium position and angle 0 is very small. ww ww

Answer 1

page 1

- The Free body has an arkaitary from Ranilubrium figure. diagram is constructed angulas displacement o position as shown in 0 m 24/ ka o Now takiny about moments Të + Kat 21 , x0 x 216 + kxlxoxd, so de sosing 13 l I distorce. spris displacement Stiffics I ö i 4 m41² q restoping split into two components 1. Pusing parallel ones theoam 2. 1. MfP+ ml = m ë for attached mass .. moment = Spaing stiffness & deflection . x perpendiculas I destance. a sino x aughh for sunal angles sinto . deflection

page 2

- so Now deftecton simplifying = Oxlength. our het moment about mko't med et ke wtho + k, l o so = sme ö + (46+K) elle =0, öt 4let ki-0. (som de ( dividing 6 5m a) Governing Equation as Equation of motion » öt 4kqtlar o=o. sm 1 sm b. meq=5m S - leq a 4k, the (denominator of 4 kz tky in the equation of motion] numeratae of kkątki sm c. angular desquency w fazt 5m. meg

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