D12 Option 82 (Fig. 8 cond. 2) teormeh Targ SM 1989

The finished solution of the D12 Option 82 on the theoretical mechanics of Targa SM 1989 .. Conditions to task Dynamics 12 (p. 101 Targa in the training manual): The mechanism located in the vertical plane (Fig. D12.0 - D12.9) consists of step 1 and 2 wheels with radii R1 = 0,4 m, r1 = 0,2 meters, R2 = 0,5 m, r2 = 0,3 m having a fixed rotational axis; 3 homogeneous rod length l = 1,2 m fixed hinge at one end; loads 4 and 5 are suspended from the yarns wound on wheels. In the distance the rod AB = 2l / 3. The rod 3 is connected to the wheel 2 weightless rod 6. The wheels 1 and 2 and are engaged with (Fig. 0-4), or are connected by a weightless rod 7 (Fig. 5-9). To the wheel and the rod 3 attached spring. Table. D12 given mass mi bodies (kg) and the spring stiffness coefficients ci (n / m). Dashes in the columns of the table indicate that the relevant body or in the spring system is not included (in the figure the body and do not depict the spring); As a result, each embodiment becomes quite simple mechanism comprising three or even two bodies. The rod 6 or 7 is a part of the mechanism when it includes two bodies connected by this terminal. In the position shown in Figures, the mechanism is in equilibrium. To determine the frequency and the period of small oscillations about the equilibrium position. Find also, what is the static elongation (compression) spring λst in equilibrium. When calculating the count wheels 1 and 2 of homogeneous solid cylinder of radius R1 and R2, respectively. Consider two examples of solving this problem.

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