k₁m₁k₂m₂System of masses and springs. Consider a system of two toy railway cars (i.e., frictionless masses) connectedto each other by two springs, one of which is attached to the wall, as shown inthe figure. Let x₁ and x₂ be the displacement of the first and second massesfrom their equilibrium positions. Suppose the masses are m₁ = 10 kg andm₂ =5 kg, and the spring constants are k₁ = 180 N/m and k₂ = 90 N/m.a. Set up a system of second-order differential equations that models this situation.X=-277.29-18Xk₁T^^^^^.PWT^^^^.PWWWVSystem of masses and springs.b. Find the general solution to this system of differential equations. Use a₁, a2, b₁, b2 todenote arbitrary constants, and enter them as a1, a2, b1, b2.x₁ (t) = (1/2)a1 cos(3t)+(1/2)b1sin(3t)-a2cos(6t)-b2sin(6t)x₂(t) = a1cos(3t)+b1sin(3t)+a2cos(6t)+b2sin(6t)

In Hooke's law of elasticity, the displacement or size of the deformation is directly proportional…

Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x₁ and x₂ be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m₁ 10 kg and = m2 5 kg, and the spring constants are k₁ 180 N/m and k₂ = 90 N/m. = x = a. Set up a system of second-order differential equations that models this situation. -27 7.2 9 -18 = x www System

Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x₁ and x₂ be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m₁ 10 kg and = m2 5 kg, and the spring constants are k₁ 180 N/m and k₂ = 90 N/m. = x = a. Set up a system of second-order differential equations that models this situation. -27 7.2 9 -18 = x www System