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 = 6 kg and m₂ = 3 kg, and the spring constants are k₁ = 192 N/m and k₂ = 96 N/m. a. Set up a system of second-order differential equations that models this situation. → 11 k₁ m₁ k₂ m₂ System of masses and springs.
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 = 6 kg and m₂ = 3 kg, and the spring constants are k₁ = 192 N/m and k₂ = 96 N/m. a. Set up a system of second-order differential equations that models this situation. → 11 k₁ m₁ k₂ m₂ System of masses and springs.
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Transcribed Image Text: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 = 6 kg and
m₂ = 3 kg, and the spring constants are
k₁ = 192 N/m and k₂ = 96 N/m.
a. Set up a system of second-order differential equations that models this situation.
k₁
www
k₂
www
System of masses and springs.
m1
m2
b. Find the general solution to this system of differential equations. Use a₁, a2, b₁,b2 to denote arbitrary
constants, and enter them as a1, a2, b1,b2.
x₁ (t) =
x₂ (t) =
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