Purchase Solution

Lagrangian Mechanics Question

Not what you're looking for?

Ask Custom Question

Consider a bead of mass m sliding without friction on a straight wire that passes through the origin and is inclined from the vertical by a constant angle alpha. The wire is being spun with constant angular velocity w about its vertical axis as shown in the figure. The bead is attached to the origin with a spring of force constant k as shown, with the unstretched length of the spring assumed to be zero. A characteristic frequency of the problem is thus w = sqrt(k/m).

Choose for generalized coordinate the distance r of the mass from the origin, and solve for its motion by the Lagrangian method. Your solution should clearly exhibit the following steps:
i) Write down expressions for the kinetic energy T and the potential energy U.
ii) Write down the Lagrangian.
iii) Write down the Lagrange equation of motion for r.
iv) Solve the Lagrange equation of motion.
v) Discusses the conditions under which there is a position of stable equilibrium, and the frequency of small oscillations about this position.
vi) Discuss the motion when there is not a position of stable equilibrium.
vii) Discuss relevant limiting cases for the parameters of the problem.

Purchase this Solution

Solution Summary

PDF attached answers 7 questions on a bead sliding on a wire, including the Lagrangian equation of motion and conditions for a stable equilibrium.

Purchase this Solution

Free BrainMass Quizzes
Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Basic Physics

This quiz will test your knowledge about basic Physics.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.