Parabola is a curve formed by the intersection of the cone with a plane which rests on both sides of an axis of the symmetry. In a case where the parabola is vertical, a line is drawn to one side (labeled as the directrix) will also stand vertically. On the contrary, if the line is horizontal, the directrix will also be set in a horizontal position. To expand the equation, the axis of symmetry features two major points. One of these is called the focus of the parabola, placed usually inside the parabola; the other is termed as the vertex, which rests right on the tip of the parabola, free to change direction. This concept holds immense importance in as it is used in many applications in the calculation.
Parabola is an important topic of mathematics and is quite complex to be understood by the students as they are still in the learning phase of the concept. In a parabola, the concept of curves and planes puzzle the student’s mind as they are unaware of the proper pattern of executing it. Don’t worry, at EssayCorp our team of geometry experts are always does their best to provide the top quality parabola assignment help to the students before the deadline.
Parabola has many geometric properties, but its reflection property is quite important among all. It is extensively used in satellite dishes and car headlights as their designed in such a way so that their cross sections are parabolic in shape. A car headlight is focused directly as it emits light from one source only but also has the ability to focus that light into a beam so that it does not move in all directions. On the contrary, satellite dishes do the reverse as it collects the electromagnetic rays and focuses them at one point, thus attaining a strong signal. This property of parabola plays a crucial role in understanding the concepts and equation of the parabola. Our parabola assignment help experts are always ready to help students so that they can get a proper understanding of this property of parabola in an efficient manner.
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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]