3. (30) A railroad car of mass m = 1500 kg is to be coupled to an assembly of two precoupled identical railroad cars. Th

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3 30 A Railroad Car Of Mass M 1500 Kg Is To Be Coupled To An Assembly Of Two Precoupled Identical Railroad Cars Th 1 (81.99 KiB) Viewed 36 times

3. (30) A railroad car of mass m = 1500 kg is to be coupled to an assembly of two precoupled identical railroad cars. The coupler between cars 2 and 3 is an elastic connection of stiffness k = 4.2 *107 N/m. The first car is rolled toward the other cars with a velocity of 7 m/s, as shown in Figure. It gets rigidly coupled to second car with a plastic impact so that the initial velocity of cars 1 and 2 combined becomes 3.5 m/s. a. Find the natural frequencies and the modes shapes of the system b. Determine the motion of the railroad cars x(t) =[x₁(t) x₂(t)], after coupling is achieved. 1500 kg O 7 m/s m m 1500 kg (a) 2₁ k (b) O m MO ¹2 1500 kg k = 4.2 x 107 N/m