Explore BrainMass
Share

Lagrange of a simple pendulum

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

A pendulum consists of a mass m suspended by a massless spring with unextended length of b and spring constant k. Find Lagrange's equation of motion. Assume that the pendulum is constrained to swing in a single plane.

© BrainMass Inc. brainmass.com October 16, 2018, 7:41 pm ad1c9bdddf
https://brainmass.com/physics/classical-mechanics/lagrange-of-a-simple-pendulum-123642

Attachments

Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.
================================================================

Let the generalized coordinates be (r, θ).

Kinetic Energy T= 1/2 m ( )
Potential Energy V = 1/2 k (r-b)2 - mg ( r cos θ)

Lagrange, L = T - V = 1/2 m ( ) - 1/2 k (r-b)2 + mg ( r cos θ)

L = 1/2 m ( ) - 1/2 k (r-b)2 + mg ...

Solution Summary

Equation of motion for a simple pendulum was developed starting from the generalized coordinates. Two cases were discussed. First the case of a simple pendulum was analyzed. Then the case of a pendulum oscillating vertically was analyzed. Very detailed solution is provided in a 3-page word document. Please download this question/answer pair if you are interested in understanding how to solve classical mechanics problems using Lagrange method.

$2.19
Similar Posting

Lagrangian for a Simple Pendulum

Problem:
A) Write the Lagrangian for a simple pendulum consisting of a mass m suspended at the end of a massless string of length l. Derive the equation of motion from the Euler-Lagrange equation, and solve for the motion in the small angle approximation.
B) Assume the massless string can stretch with a restoring force F=-k(r-ro) where ro is the unstretched length. Write the new Lagrangian and find the equations of motion.

View Full Posting Details