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 ₁ and ₂ 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 = 80 N/m and k₂ = 40 N/m. a. Set up a system of second-order differential equations that models this situation. ⠀ 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) = k₂ wwwwwwwwww 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 ₁ and ₂ 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 = 80 N/m and k₂ = 40 N/m. a. Set up a system of second-order differential equations that models this situation. ⠀ 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) = k₂ wwwwwwwwww System of masses and springs.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 ₁ and ₂ 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 = 80 N/m and k2 = 40 N/m.
a. Set up a system of second-order differential equations that models this situation.
⠀
x
#
#
x
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) =
#
k₁
m₁
k₂
m₂
System of masses and springs.
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