The figure shows a system of masses. The mass of 2m is connected to an immobile wall with a spring of constant 2k, while the mass of m is connected to an immobile wall with a spring of constant k. The masses are then coupled to each other with an elastic band of length L, under tension T =2kL. The masses are constrained to move in the x direction only. At equilibrium. the masses have the same x position and the springs are uncompressed. There is no friction or gravity. The displacements from equilibrium are small enough (x1, x2 << L), so that the tension in the band stays constant. 1-Write down the coupled differential equations describing the displacement of the masses from equilibrium {x1, x2}.
The figure shows a system of masses. The mass of 2m is connected to an immobile wall with a spring of constant 2k, while the mass of m is connected to an immobile wall with a spring of constant k. The masses are then coupled to each other with an elastic band of length L, under tension T =2kL. The masses are constrained to move in the x direction only. At equilibrium. the masses have the same x position and the springs are uncompressed. There is no friction or gravity. The displacements from equilibrium are small enough (x1, x2 << L), so that the tension in the band stays constant. 1-Write down the coupled differential equations describing the displacement of the masses from equilibrium {x1, x2}.
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