Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by three springs, two of which are attached to walls, as shown in the figure. Let ₁ and ₂ be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m₁ = 4 kg and m₂ = 4 kg, and the spring constants are k₁ = 256 N/m, k₂ = 384 N/m, and k3 = 256 N/m. Z" = Set up a system of second-order differential equations that models this situation. -160 x₁ (t) x₂ (t) 96 -1 1 help (matrices) Find the general solution to this system of differential equations. 1 1 96 help (formulas) help (matrices) -160 www. System of masses and springs. T a₁ cos(256t m₁ (a₂ cos (64t m₂ + b₁ sin (256t + b₂ sin (64t +

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Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.