A conservative mechanical system consists of a mass m that is constrained to move along a circle of radiusR. The centre of the circle is at the origin O of the coordinate system. The mass is connected to a point Aalong the â-axis at a distance 2R from the centre of circle with a spring of elastic constant k, so that thecorresponding elastic potential has the form Vspring = (k/2)ď², where d is the (varying) distance between themass and point A. Gravity acts, as usual, along the vertical direction. See the figure for a depiction of thesystem.0m(b) Write down the Lagrangian of the system.(a) How many degrees of freedom does the system have? Indicate generalised coordinates to describe themotion of the system.X(c) Write down the corresponding Euler-Lagrange equation(s).

Given: To find: Degree of freedom Lagrangian Euler-Lagrange equation

A conservative mechanical system consists of a mass m that is constrained to move along a circle of radius R. The centre of the circle is at the origin O of the coordinate system. The mass is connected to a point A along the î-axis at a distance 2R from the centre of circle with a spring of elastic constant k, so that the corresponding elastic potential has the form Vspring = (k/2)d², where d is the (varying) distance between the mass and point A. Gravity acts, as usual, along the vertical direction. See the figure for a depiction of the system.

A conservative mechanical system consists of a mass m that is constrained to move along a circle of radius R. The centre of the circle is at the origin O of the coordinate system. The mass is connected to a point A along the î-axis at a distance 2R from the centre of circle with a spring of elastic constant k, so that the corresponding elastic potential has the form Vspring = (k/2)d², where d is the (varying) distance between the mass and point A. Gravity acts, as usual, along the vertical direction. See the figure for a depiction of the system.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.57P: Find the stable equilibrium position of the system described in Prob. 10.56 if m = 2.06 kg.

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