Three masses, m; 3 kg, m2 5.5 kg, and m3 = 2 kg, are attached to springs, k1 = 50 N/m, k2 = 35 N/m, k3 25 N/m, and k4 = 20 N/m, as shown below. 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 to an equilibrium position as shown. The equilibrium equations of the %3D %3D !3! !3! %3D three masses are:

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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Three masses, m = 3 kg, m2 = 5.5 kg, and m3 = 2 kg, are attached to springs, k1 =
50 N/m, k2 = 35 N/m, k3 25 N/m, and k4 20 N/m, as shown below. 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 to an equilibrium position as shown. The equilibrium equations of the
%3D
%3D
%3D
three masses are:
k k
(k; + k2 +k3)u, - kzu2 = m18
- kzu, + (k3 + k4)u2-kauz = m2g
-k quz + kauz = m3g
%3D
71
k
m2
k
m2
%3D
m3
where us, uz, and us are the relative displacement of each mass as shown.
Determine the displacement of the three masses. (g = 9.81 m/s)
Answers in four do
Transcribed Image Text:Three masses, m = 3 kg, m2 = 5.5 kg, and m3 = 2 kg, are attached to springs, k1 = 50 N/m, k2 = 35 N/m, k3 25 N/m, and k4 20 N/m, as shown below. 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 to an equilibrium position as shown. The equilibrium equations of the %3D %3D %3D three masses are: k k (k; + k2 +k3)u, - kzu2 = m18 - kzu, + (k3 + k4)u2-kauz = m2g -k quz + kauz = m3g %3D 71 k m2 k m2 %3D m3 where us, uz, and us are the relative displacement of each mass as shown. Determine the displacement of the three masses. (g = 9.81 m/s) Answers in four do
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