How Do Coupled Adiabatic Pendula Behave?

[Hamsi]

Homework Statement

An adiabatic pendulum (right) is coupled via a spring with spring contant κ to a normal non-variable pendulum. The pendula have equal mass m and, initially, equal length l . The right pendulum is adiabatically pulled up with frequency ω(t)

1. Derive the equations of motion for this system
2. Which instantaneous frequency Ω(t) does the coupled system support at a given time t?

Relevant Equations

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Homework Statement: An adiabatic pendulum (right) is coupled via a spring with spring contant κ to a normal non-variable pendulum. The pendula have equal mass m and, initially, equal length l . The right pendulum is adiabatically pulled up with frequency ω(t)

1. Derive the equations of motion for this system
2. Which instantaneous frequency Ω(t) does the coupled system support at a given time t?
Homework Equations: -

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[Chestermiller]

What is an adiabatic pendulum?