A light rigid rod of length 9L, shown in its static position in the figure below,...

 

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A light rigid rod of length 9L, shown in its static position in the figure below, is more connected at point O and carries masses M and 2m at the indicated position. The motion of the bar is constrained by a spring with stiffness k and a damper with coefficient c, and the clockwise direction is positive. H The expression lo for the moment of inertia of the system with respect to 0 is derived. e If the equation of motion of the system takes the form O+ A + B 0=0, determine the expressions for the coefficients A and b in terms of k, c and m. If the property of the system is M = 9kg, C = 378NSM-1, k= 2.767 KNM-1, and determine the values of A and b. ww E Derive an expression for the motion of the rod if it is given a small initial angular displacement, 00. + ( If a second damper with coefficient C1 is added to the system and placed directly below the mass m, at the left end of the bar, the value of C1 is calculated to ensure that the system does not have an oscillatory response when perturbed. m 31 Ꮎ 31 2m 31 k M A light rigid rod of length 9L, shown in its static position in the figure below, is more connected at point O and carries masses M and 2m at the indicated position. The motion of the bar is constrained by a spring with stiffness k and a damper with coefficient c, and the clockwise direction is positive. H The expression lo for the moment of inertia of the system with respect to 0 is derived. e If the equation of motion of the system takes the form O+ A + B 0=0, determine the expressions for the coefficients A and b in terms of k, c and m. If the property of the system is M = 9kg, C = 378NSM-1, k= 2.767 KNM-1, and determine the values of A and b. ww E Derive an expression for the motion of the rod if it is given a small initial angular displacement, 00. + ( If a second damper with coefficient C1 is added to the system and placed directly below the mass m, at the left end of the bar, the value of C1 is calculated to ensure that the system does not have an oscillatory response when perturbed. m 31 Ꮎ 31 2m 31 k M