Final answer:
The correct principle used to analyze the motion of a double pendulum is D'Alembert's Principle, which is not related to buoyancy, elasticity, or fluid pressure but to inertial forces in dynamic systems. so, option C is the correct answer.
Step-by-step explanation:
In the context of a double pendulum's motion, C) D'Alembert's Principle is commonly used to analyze its motion. This principle, which is an application of Newton's second law of motion, allows us to treat dynamic problems as if they were static by introducing the concept of inertial force. With a double pendulum, the chaotic and complex motion arises due to the gravitational restoring forces acting on the masses of the pendulum. D'Alembert's Principle enables physicists to write equations of motion that can be solved to predict the pendulum's behavior.
Archimedes' Principle, another important concept in physics, is unrelated to the motion of a pendulum. Archimedes' Principle states that the buoyant force on an object equals the weight of the fluid it displaces, which is crucial in fluid mechanics. Hooke's Law provides a mechanism to predict the restoring force in a system where an elastic spring is deformed. Lastly, Pascal's Law is related to the pressure distribution in a fluid.
The correct principle for analyzing double pendulum motion is not related to buoyancy, elasticity, or fluid pressure, but rather the inclusion of inertial forces in the system's dynamics.