A point-like mass is constrained to move along the z-axis only. It is attached to two springs, each of spring constant k, and each of rest length 0. One spring has one of its ends fixed at x = 0 and y = h; the other spring is fixed at one end to x = 0 and y=-h as shown in the figure below. Gravity does not act on the system. The springs do not bend but contract and extend along straight lines between their end points. y h (a) How many degrees of freedom does the system have? (b) Write down the Lagrangian of the system. www. (c) Write down the corresponding Euler-Lagrange equation(s). m

A point-like mass is constrained to move along the z-axis only. It is attached to two springs, each of spring constant k, and each of rest length 0. One spring has one of its ends fixed at x = 0 and y = h; the other spring is fixed at one end to x = 0 and y=-h as shown in the figure below. Gravity does not act on the system. The springs do not bend but contract and extend along straight lines between their end points. y h (a) How many degrees of freedom does the system have? (b) Write down the Lagrangian of the system. www. (c) Write down the corresponding Euler-Lagrange equation(s). m

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 19P: A light spring with spring constant 1 200 N/m is hung from an elevated support. From its lower end...

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