Question

A light nextensible rod OA of length is attached to the point O and free to rotate smoothly around that point. At the other end of the rod, a second light rod BC is attached such that it is always at right angles to the rod OA. A bead of mass m is free to move smoothly along BC un der the influence of an elastic force i.e. a spring of natural length zero) directed towards A. The system is subject to a gravitational acceleration g acting vertic- ally downwards. Assume that all objects are confined to a particular vertical plane, that the bead can pass through the point A, and that the bead never falls off the rod BC B

a)How many degrees of freedom are there in the system?

(b) Using appropriately-defined generalized coordinates, find the kinetic and potential
energies of the system.

(c) Write down the mass–inertia matrix for the system, and find the configurations for
which the Lagrangian is not regular.

(d) Find the equations of motion for the system

Answer 1

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