4.31 Three masses, m₁ = 2 kg, m₂ = 3 kg, and m3 = 1.5 kg, are attached to = 20 N/m, and k₁ = 15 N/m, as springs, k, = 30 N/m, k₂= 25 N/m, k3 shown. Initially the masses are positioned such that the springs are in their nat- ural length (not stretched or compressed); then the masses are slowly released and move downward to an equilibrium position as shown. The equilibrium equations of the three masses are: (k₁+k₂ + kg)u₁-kzU₂ = m₁g - k3u₁ + (k3+k₁)u₂-k4u3 = m₂g ky 3 kiş 7222 73 Uy M m M -k4u₂+k4l3 = mzg where u₁, ₂, and u, are the relative displacement of each mass as shown. Determine the displacement of the three masses. (g = 9.81 m/s²)

4.31 Three masses, m₁ = 2 kg, m₂ = 3 kg, and m3 = 1.5 kg, are attached to = 20 N/m, and k₁ = 15 N/m, as springs, k, = 30 N/m, k₂= 25 N/m, k3 shown. Initially the masses are positioned such that the springs are in their nat- ural length (not stretched or compressed); then the masses are slowly released and move downward to an equilibrium position as shown. The equilibrium equations of the three masses are: (k₁+k₂ + kg)u₁-kzU₂ = m₁g - k3u₁ + (k3+k₁)u₂-k4u3 = m₂g ky 3 kiş 7222 73 Uy M m M -k4u₂+k4l3 = mzg where u₁, ₂, and u, are the relative displacement of each mass as shown. Determine the displacement of the three masses. (g = 9.81 m/s²)

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Chapter1: Units, Trigonometry. And Vectors

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Question

4.31 Three masses, m, = 2 kg, m₂
3 kg, and m₂ = 1.5 kg, are attached to
= 15 N/m, as
springs, k, = 30 N/m, k₂= 25 N/m, k, = 20 N/m, and k₁
shown. Initially the masses are positioned such that the springs are in their nat-
ural length (not stretched or compressed); then the masses are slowly released
and move downward to an equilibrium position as shown. The equilibrium
equations of the three masses are:
(k₁+k₂ + K3)U₁ - k3u₂ = m₁g
-k₂u₁ + (k3+k₁)u₂-k₁u3 = m₂g
-K4U₂ + kallz
= m3g
where u₁, ₂, and u, are the relative displacement of each mass as shown. Determine the displacement of
the three masses. (g
9.81 m/s²)
H
m
7722
M3
u
4th
297
m₂
M₁

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