Algebra is one of the most basic and important part of mathematics which deals with calculations that make the use of variables. Moreover, it is a study of algebraic equations that includes the polynomial function of one or more variables. The basic part of algebra is considered as elementary algebra and the advanced part of algebra is called abstract algebra or modern algebra. Elementary algebra is required in the analysis of science and engineering, whereas abstract algebra is a vast area of advanced mathematics.
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÷) which are applied to the set of variables, e.g:
(x+y-z), including the formulation of the equation, this type of algebra also permits the formulation of a functional relationship like
f(x)= 5x - 10, where
fis the function and
xis the number to which the function is applied.
5x2+6x+2=0, where the highest power of the variable is a square is called a quadratic equation. A quadratic equation is in the form of;
f(x)= ax2+bx+c, where
y=2x+7. Our algebra assignment help provides the best help on this mathematical topic and many others, we service from the easiest to the toughest topics in algebra assignment.
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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]