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3. A uniform solid disk with mass m and radius r rotates without friction around the horizontal axis O with angular velocity ω0. A belt with two weights (each of them with mass M=2m) is thrown over the disk. Assuming that the initial velocities of the weights are zero, determine the speed with which they will move after slipping of the belt on the disk finishes. Find the friction work. 9. An Euler-Bernoulli cantilever beam with a load P at the end is given. Moment of inertia J of the cross-section and Young's modulus E of the material is constant along the entire length l of the beam. Determine the deflection of the beam at the point where force P is applied: 1) solving the differential equation; 2) using Castigliano's method; 3) using Ritz method (keep only one term in the expansion, and compare with the exact solution).
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