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The exact geometry definition lies in the term itself which means the measurement of earth. A mathematician who works in the field of geometry is called a geometer. Geometry studies shapes, properties, angles, lines etc. It deals with flat, two dimensional and three dimensional shapes. EssayCorp provides the best geometry help online free answers.
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In the vast field of technology, the importance of geometry has been increased to a greater extent. There are some applications of geometry that are useful in following fields:
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Three particles A, B and C lie in that order in a straight smooth groove so that they can only move along the x-axis. Both A and C are of unit mass whilst B is of mass M. Particle B is joined to the other two by identical linear springs of unit stiffness.
(a) If the three particles are displaced from equilibrium by distances x1, x2 and x3 show that the equations of motion are d2x1/dt2 = x2 - x1, M d2x2/dt2 = x3 - 2x2 + x1, d2x3/dt2 = x2 - x3.
(b) Prove that the frequencies of the three normal modes are given by ? = 0, 1 and ?2 = 1 + (2/M). [5 marks]
(c) Describe the motions of the particles corresponding to the normal modes.[4 marks]