Three masses, m₁ = 2.5 kg, m₂ = 3 kg, and m3 = 1 kg, are attached to springs with stiffness constants, k₁ = 3 kN/m, k₂= 3.5 kN/m, k3 = 2 kN/m, and k4 = 2.5 kN/m, as shown in the figure. Initially the masses are positioned such that the springs are in their natural length (not stretched or compressed); then the masses are slowly released and move downward due to gravity, such that the springs are stretched to their equilibrium positions as shown. The equilibrium equations of the three masses are: (K₁ + K₂ + K3)U₁ - k3U₂ = m₁g -K3U₁ + (K3 + K4)U₂ -k4u3 = m₂g m

Three masses, m₁ = 2.5 kg, m₂ = 3 kg, and m3 = 1 kg, are attached to springs with stiffness constants, k₁ = 3 kN/m, k₂= 3.5 kN/m, k3 = 2 kN/m, and k4 = 2.5 kN/m, as shown in the figure. Initially the masses are positioned such that the springs are in their natural length (not stretched or compressed); then the masses are slowly released and move downward due to gravity, such that the springs are stretched to their equilibrium positions as shown. The equilibrium equations of the three masses are: (K₁ + K₂ + K3)U₁ - k3U₂ = m₁g -K3U₁ + (K3 + K4)U₂ -k4u3 = m₂g m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

I need a hand sketch diagram

=
Three masses, m₁ = : 2.5 kg, m₂
3 kg, and m₂ = 1 kg, are attached
to springs with stiffness constants, k₁ = 3 kN/m, k₂ = 3.5 kN/m,
k3 = 2 kN/m, and k4 = 2.5 kN/m, as shown in the figure. Initially
the masses are positioned such that the springs are in their natural
length (not stretched or compressed); then the masses are slowly
released and move downward due to gravity, such that the springs
are stretched to their equilibrium positions as shown. The
equilibrium equations of the three masses are:
(K₁ + K₂ + K3)U₁ - K3U₂ = m₁g
-K3U₁ + (K3 + K4)U₂ - k4u3 = m₂g
-K4U₂ + K4U₂ = m3g
k₁3
m₁
k33
m₂
K4
m₁
k₂
F U1₂
U13
m₁
M
m₂
M
m3
where u₁, U₂, and u3 are the relative displacement of each mass as shown. The gravitational constant
= 9.81 m/s².
a) Derive the statics equilibrium equations using free-body diagrams and Newton's law. (Hand
sketch the free-body diagrams and then scan and paste into the homework file)

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