The binomial theorem is very important in founding the mathematical base for a student. It was observed that binomial theorem was used in the 4th Century and also in the 6th Century India. It is an important mathematical concept that has been used for centuries and a student pursuing or planning to pursue a mathematical course must to adept at it to successfully be able to meet the academic requirement. The assignment in this subject or for this concept can be problematic and a student might come across several hurdles. Therefore, we provide binomial theorem assignment help to the students in the UK, US, and Australia.
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Binomial theorem is the component of elementary algebra, which describes the algebraic expansion of powers of a binomial. The theorem states that it is possible to expand the power of
( a + b) expression into a sum involving terms of the form
ax by c; where the exponents b and c are non-negative integers with
b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b.
(x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4
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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]