This branch of mathematics is pivotal for the study of height and its relationship with angles of triangles. It originated in the 3rd century BC; it has a major application in geometry and astronomical studies. Students find this subject tough, because of its convoluted concepts and formulas. It is a complex subject and very difficult to master. The assignments and homework on this subject can be the cause of worry for the students. Therefore, we at EssayCorp provide assignment assistance to students all around the world. Our trigonometry assignment help service is reputed to help the students gain the best grades. We have expert writers who write your assignment. These writers are based from all around the world, they are experienced and can provide the best conclusion to your assignment.
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The trigonometric functions were first derived by the astronomers of the 3rd century. They noted that the length of the sides of a right-angle triangle and the angles between the sides have a fixed relationship. If the length of any one side and anyone angle is known than the other lengths and angle value can be found out algorithmically. Trigonometry started as the computational segment of geometry. For example, one announcement of plane geometry states that a triangle is controlled by a side and two plots. As such, provided for one side of a triangle and two plots in the triangle, then the other two sides and the remaining edge are resolved. Trigonometry incorporates the techniques for processing those other two sides. The remaining point is not difficult to discover since the entirety of the three edges rises to 180 degrees.
Maths is a subject that is known to be the most disliked subject among students. But, given its importance and the requirement of academic institutions, a student cannot get rid of this subject. The assignments in this subject are a necessity and must be given due importance.
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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]