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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Static and Kinetic Friction

Kinetic friction comes into existence when there are moving surfaces means in other words we can say that the force which comes into existing between moving surfaces is known as kinetic friction.

Question

TIL
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
(b) Write down the Lagrangian of the system.
h
(a) How many degrees of freedom does the system have?
wwww
(c) Write down the corresponding Euler-Lagrange equation(s).
m
X

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