Problem 1State the number of degrees of freedom for the following systems. In each case, indicate the appropriategeneralised coordinates that can be used to describe the motion. You cannot simply state that the generalisedcoordinates are "x", "0" etc. Instead, you should specify them using diagrams.(a) A particle constrained to move on a fixed wire.(b) A simple pendulum contained in the vertical (â, ý) plane. The suspension point of the pendulum is freeto move on the horizontal x axis.(c) A charged particle moving in a constant background magnetic field. The field is pointing in the vertical2 direction.(d) A system of two particles, both of which are constrained to move along a ring of radius R. A springof elastic constant k is stretched between two particles and the potential is V = kd² where d is thedistance between the two particles.(e) A particle constrained to move on the surface z = x² + y²(Here x, y, z are Cartesian coordinates).

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State the number of degrees of freedom for the following systems. In each case, indicate the appropriate generalised coordinates that can be used to describe the motion. You cannot simply state that the generalised coordinates are "x", "0" etc. Instead, you should specify them using diagrams. (a) A particle constrained to move on a fixed wire. (b) A simple pendulum contained in the vertical (2, ý) plane. The suspension point of the pendulum is free to move on the horizontal r axis. (c) A charged particle moving in a constant background magnetic field. The field is pointing in the vertical 2 direction. (d) A system of two particles, both of which are constrained to move along a ring of radius R. A spring of elastic constant k is stretched between two particles and the potential is V = kd² where d is the distance between the two particles. (e) A particle constrained to move on the surface z = x² + y² (Here x, y, z are Cartesian coordinates).

State the number of degrees of freedom for the following systems. In each case, indicate the appropriate generalised coordinates that can be used to describe the motion. You cannot simply state that the generalised coordinates are "x", "0" etc. Instead, you should specify them using diagrams. (a) A particle constrained to move on a fixed wire. (b) A simple pendulum contained in the vertical (2, ý) plane. The suspension point of the pendulum is free to move on the horizontal r axis. (c) A charged particle moving in a constant background magnetic field. The field is pointing in the vertical 2 direction. (d) A system of two particles, both of which are constrained to move along a ring of radius R. A spring of elastic constant k is stretched between two particles and the potential is V = kd² where d is the distance between the two particles. (e) A particle constrained to move on the surface z = x² + y² (Here x, y, z are Cartesian coordinates).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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