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A bead of mass m is threaded on a frictionless circular
Chapter 11, Problem 11.26(choose chapter or problem)
A bead of mass m is threaded on a frictionless circular wire hoop of radius R and mass m (same mass). The hoop is suspended at the point A and is free to swing in its own vertical plane as shown in Figure 11.20. Using the angles q51 and 02 as generalized coordinates, solve for the normal frequencies of small oscillations, and find and describe the motion in the corresponding normal modes. [Hint: The KE of the hoop is .1. Iii , where I is its moment of inertia about A and can be found using the parallel axis theorem.]
Questions & Answers
QUESTION:
A bead of mass m is threaded on a frictionless circular wire hoop of radius R and mass m (same mass). The hoop is suspended at the point A and is free to swing in its own vertical plane as shown in Figure 11.20. Using the angles q51 and 02 as generalized coordinates, solve for the normal frequencies of small oscillations, and find and describe the motion in the corresponding normal modes. [Hint: The KE of the hoop is .1. Iii , where I is its moment of inertia about A and can be found using the parallel axis theorem.]
ANSWER:Step 1 of 9
The state of given physical system can be described by applying the Lagrangian function to system, it is expressed as
L=T-V
Here, T is the kinetic energy of the system and V is the potential energy of the system.
The Lagrangian function of a system having generalized coordinates is 
Then the Lagrange’s equations for this conservative system can be expressed as,
