PROBLEM 10.80 A slender rod AB, of mass m, is attached to two blocks AandBthat can move freely in the guides shown. Knowing that the spring is unstretched when ABis horizontal, determine three values of θcorresponding to equilibrium when 125 kg,m=320 mm,l=and 15 kN/mm.k=State in each case whether the equilibrium is stable, unstable, or neutral. SOLUTION Using the results of Problem 10.79, particularly the condition of equilibrium ()()cossincos1 1tan02mgklθθ+−−−=Now, with 2125 kg 9.81 m/s1226.25 N, 320 mm,Wmgl====and 15 kN/m,k=Now ()1226.25 N1.277322 15000 N/m 0.32 mWklso that ( )( )cossincos1 1tan1.27730+−=By inspection, one solution is cos0 or 90.0==°Solving numerically: 0.38338 rad9.6883 and 0.59053 rad33.8351°°Stability ()()2221cossincossinsincos1sincossin
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