Problem 2: Consider the following system of two interconnected pendulums P₁ and P₂ with same mass m and length 2α that are suspended with massless rods from O₁ and O₂ without friction as shown in Fig. 2. The spring k is unstreched when the pendulums are at rest in vertical equilibrium. A horizontal force f(t) is applied on the mass m of the pendulum P₁. f(t) P₁ a a m a P₂ m Fig. 2: Interconnected pendulums Assuming small angles write the linearized equations of motion of the two pendulums with respect to the angular displacements of the pendulum P₁ and 2 of the pendulum P₂

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Problem 2: Consider the following system of two interconnected pendulums P₁ and P₂ with same mass m and
length 2α that are suspended with massless rods from O₁ and O₂ without friction as shown in Fig. 2. The spring
k is unstreched when the pendulums are at rest in vertical equilibrium. A horizontal force f(t) is applied on the
mass m of the pendulum P₁.
f(t)
P₁
a
a
m
a
a
P₂
Fig. 2: Interconnected pendulums
Assuming small angles write the linearized equations of motion of the two pendulums with respect to the angular
displacements of the pendulum P₁ and ₂ of the pendulum P₂
Transcribed Image Text:Problem 2: Consider the following system of two interconnected pendulums P₁ and P₂ with same mass m and length 2α that are suspended with massless rods from O₁ and O₂ without friction as shown in Fig. 2. The spring k is unstreched when the pendulums are at rest in vertical equilibrium. A horizontal force f(t) is applied on the mass m of the pendulum P₁. f(t) P₁ a a m a a P₂ Fig. 2: Interconnected pendulums Assuming small angles write the linearized equations of motion of the two pendulums with respect to the angular displacements of the pendulum P₁ and ₂ of the pendulum P₂
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