Question

for the range of oso a 180, find the locations of equilibrium of the system and mention in whether the equilibrium is stable, Unstable neutral. each case Oy 1.58 fig. I: Two uniform rods of mass m and length, e attached to gears are 3 20

Answer 1

solution - 0 A 1:50 1/2 61.50 3C O V- Orangle Now the potential energy of the system using the relation w (la cost. 50) +Cleoso) W: weight of the rod a= length of the rod Now we are equate the post dilferentiahon o eqo du Here Substtute w llacost-58) tw (lecaso) for v d (w( 42.005 1-50)+7 (4260)) do 2 (-1.5511150) + we c-Sino) coce crossin 1.50 +sino)-0 -wl 1.55in 1.50 +Sin B co The above equahon long the trail anderror procedure The value o are oo and 137.8° Now find the second differenhaton of equatu we (2.25 cas 1.50 ecosos dos find the stabilly at o=0°

plow Substfele o for o en eg2 dru wl dor (2.25 Coslis -5 (0°) + cos0°)) :- (2.25+1) = (3.25)we co 2 unstable for 0° Now find the stability, at 0= 137 of° O= 137° 8° in equchon du dor Woul (2.25 Cosi. 50137.5") + Cos (137680)) WL (2.75) = (2-75) we so Stable for 137-8e

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