D The linkage shown (Exercise 7.30) is braced by a spring of stiffness k in order...

 

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D The linkage shown (Exercise 7.30) is braced by a spring of stiffness k in order to support the force P that acts vertically downward at point D. Point A of link AC' is a stationary, frictionless pin and the spring is unstretched when 0 = 45°. The system lies in the vertical plane so gravitational potential energy must be considered in addition to the potential energy due to the spring. The mass of link AC is m and the mass of link BD is 3m/2. Both links can be considered as slender, uniform rods. (a) Give expressions for the kinetic and potential energies of the system in terms of the generalized coordinate 0. (b) Give the generalized force associated with force P for the generalized coordinate 0. P L L/2 B Exercise 7.30 Problem 2. 3 (a) T = ²m1²0² (25+² sin²0); 24 (b) Qe = --PLcose 2 13 =kL² (2cos0 - √2)² + ¹3³ mgLsine V 8 D The linkage shown (Exercise 7.30) is braced by a spring of stiffness k in order to support the force P that acts vertically downward at point D. Point A of link AC' is a stationary, frictionless pin and the spring is unstretched when 0 = 45°. The system lies in the vertical plane so gravitational potential energy must be considered in addition to the potential energy due to the spring. The mass of link AC is m and the mass of link BD is 3m/2. Both links can be considered as slender, uniform rods. (a) Give expressions for the kinetic and potential energies of the system in terms of the generalized coordinate 0. (b) Give the generalized force associated with force P for the generalized coordinate 0. P L L/2 B Exercise 7.30 Problem 2. 3 (a) T = ²m1²0² (25+² sin²0); 24 (b) Qe = --PLcose 2 13 =kL² (2cos0 - √2)² + ¹3³ mgLsine V 8

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Solution a The kinetic energy of the system can be ... View the full answer