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Consider a system of two toy railway cars (.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x, and x₂ be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m₁ = 2 kg and m₂ = 1 kg, and the spring constants are k₁ = 36 N/m and k₂= 18 N/m. a. Set up a system of second-order differential equations that models this situation. -27 18 -18 www. www. b. Find the general solution to this system of differential equations. Use a,,a, b₁,b to denote arbitrary constants, and enter them as a1, a2, b1,b2. x₁ (1) == x₂ (1)==

Consider a system of two toy railway cars (.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x, and x₂ be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m₁ = 2 kg and m₂ = 1 kg, and the spring constants are k₁ = 36 N/m and k₂= 18 N/m. a. Set up a system of second-order differential equations that models this situation. -27 18 -18 www. www. b. Find the general solution to this system of differential equations. Use a,,a, b₁,b to denote arbitrary constants, and enter them as a1, a2, b1,b2. x₁ (1) == x₂ (1)==

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Consider a system of two toy railway cars (.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x, and x2 be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m, = 2 kg and m₂ = 1 kg, and the spring constants are k₁ = 36 N/m and k₂= 18 N/m. a. Set up a system of second-order differential equations that models this situation. -27 18 x₁ -18 www. www. b. Find the general solution to this system of differential equations. Use a, a, b, by to denote arbitrary constants, and enter them as a1, a2, b1,b2. (1) == x₂(t)=
Transcribed Image Text:Consider a system of two toy railway cars (.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x, and x2 be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m, = 2 kg and m₂ = 1 kg, and the spring constants are k₁ = 36 N/m and k₂= 18 N/m. a. Set up a system of second-order differential equations that models this situation. -27 18 x₁ -18 www. www. b. Find the general solution to this system of differential equations. Use a, a, b, by to denote arbitrary constants, and enter them as a1, a2, b1,b2. (1) == x₂(t)=
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