Solution of the D6 version 54 of the textbook on theoretical mechanics of manuals SM Targ 1988 (the same as the task D8 Targ 1983). Compare condition advise the task D6 (p 56 1988 SM training manual Targ.) The mechanical system consists of the bodies 1, 2, 3, 4, 5, having a weight of P1, P2, P3, P4, P5, respectively; body system linked strands wound on stepped blocks 1 and 2 (Fig. D6.0, D6.9, Table. D6). A dash in the table columns, where the weights are set, indicates that the corresponding body not included in (the figure does not depict), a zero in the columns of the table means that the body is considered weightless but in part (in the figure should be shown). For wheels, designated No. 4, P4 - their total weight (a weight of the platform carriage is not considered). The radii of the stepped blocks 1 and 2 are, respectively: R1 = R, r1 = 0,8R; R2 = R, r2 = 0,4 R. To calculate the moment of inertia both blocks, wheels and rollers considered homogeneous cylinder of radius R.
In the system other than gravity are applied to the force F. body 4 or 5 (if the body 5 is not included in the system, the force applied to a point B of the truck), and the couple of forces with the moments M1 and M2 applied to the blocks (when M <0 direction opposite to the time shown in the figure). Thread on the plot indicated in the table in the column included ;, Spring stiffness spring with a coefficient (for example, if the column should AB, AB is the portion of the spring, if the AD AD spring, etc.); at the initial time the spring is not deformed. Create for the Lagrange equations of the system and to determine the frequency of them and the period of oscillation, made system bodies while moving.