Saint Joseph’s University Online MBA Program no GMAT Essay Example

Saint Joseph’s University Online MBA Program no GMAT Essay Example Saint Joseph’s University Online MBA Program no GMAT Essay Saint Joseph’s University Online MBA Program no GMAT Essay Saint Joseph’s University  Online MBA Program no GMAT.  For over one hundred and fifty years Saint Joseph’s University has been grooming the minds and abilities of young men and women in a strong and challenging academic  atmosphere  immersed in the wonderful Jesuit tradition of  care for the entire human  being. At Saint Joseph’s University, your  scholastic  environment will be filled with  intellect,   spirit, guidance and  purpose. We respect all of your values and fully support you with a healthy learning environment that meets your educational needs. You are our first academic  priority: your mind, education, making sure your having a very positive experience with your achievements and your dreams a priority. Saint Joseph’s University is also accredited by The Middle States Association’s Commission on Higher Education, so you can take comfort and rest assured you will receive the very best online education possible. Saint Joseph’s University is proudly offering you an online bachelor’s,  master’s and certificate programs, such as Criminal Justice,  MS in Education, as well as Organization Development and   also including Business Intelligence,  Leadership and more. Click the Banner below for the Official:   Saint Joseph’s University Online MBA Program no GMAT

Mathematical Properties of Waves

Mathematical Properties of Waves Physical waves, or mechanical waves, form through the vibration of a medium, be it a string, the Earths crust, or particles of gases and fluids. Waves have mathematical properties that can be analyzed to understand the motion of the wave. This article introduces these general wave properties, rather than how to apply them in specific situations in physics. Transverse Longitudinal Waves There are two types of mechanical waves. A is such that the displacements of the medium are perpendicular (transverse) to the direction of travel of the wave along the medium. Vibrating a string in periodic motion, so the waves move along it, is a transverse wave, as are waves in the ocean. A longitudinal wave is such that the displacements of the medium are back and forth along the same direction as the wave itself. Sound waves, where the air particles are pushed along in the direction of travel, is an example of a longitudinal wave. Even though the waves discussed in this article will refer to travel in a medium, the mathematics introduced here can be used to analyze properties of non-mechanical waves. Electromagnetic radiation, for example, is able to travel through empty space, but still, has the same mathematical properties as other waves. For example, the Doppler effect for sound waves is well known, but there exists a similar Doppler effect for light waves, and they are based around the same mathematical principles. What Causes Waves? Waves can be viewed as a disturbance in the medium around an equilibrium state, which is generally at rest. The energy of this disturbance is what causes the wave motion. A pool of water is at equilibrium when there are no waves, but as soon as a stone is thrown in it, the equilibrium of the particles is disturbed and the wave motion begins.The disturbance of the wave travels, or propogates, with a definite speed, called the wave speed (v).Waves transport energy, but not matter. The medium itself doesnt travel; the individual particles undergo back-and-forth or up-and-down motion around the equilibrium position. The Wave Function To mathematically describe wave motion, we refer to the concept of a wave function, which describes the position of a particle in the medium at any time. The most basic of wave functions is the sine wave, or sinusoidal wave, which is a periodic wave (i.e. a wave with repetitive motion). It is important to note that the wave function doesnt depict the physical wave, but rather its a graph of the displacement about the equilibrium position. This can be a confusing concept, but the useful thing is that we can use a sinusoidal wave to depict most periodic motions, such as moving in a circle or swinging a pendulum, which dont necessarily look wave-like when you view the actual motion. Properties of the Wave Function wave speed (v) - the speed of the waves propagationamplitude (A) - the maximum magnitude of the displacement from equilibrium, in SI units of meters. In general, it is the distance from the equilibrium midpoint of the wave to its maximum displacement, or it is half the total displacement of the wave.period (T) - is the time for one wave cycle (two pulses, or from crest to crest or trough to trough), in SI units of seconds (though it may be referred to as seconds per cycle).frequency (f) - the number of cycles in a unit of time. The SI unit of frequency is the hertz (Hz) and1 Hz 1 cycle/s 1 s-1angular frequency (ω) - is 2Ï€ times the frequency, in SI units of radians per second.wavelength (ÃŽ ») - the distance between any two points at corresponding positions on successive repetitions in the wave, so (for example) from one crest or trough to the next, in SI units  of meters.  wave number (k) - also called the propagation constant, this useful quantity is defined as 2 Ï₠¬ divided by the wavelength, so the SI units are radians per meter. pulse - one half-wavelength, from equilibrium back Some useful equations in defining the above quantities are: v ÃŽ » / T ÃŽ » fω 2 Ï€ f 2 Ï€/TT 1 / f 2 Ï€/ωk 2Ï€/ωω vk The vertical position of a point on the wave, y, can be found as a function of the horizontal position, x, and the time, t, when we look at it. We thank the kind mathematicians for doing this work for us, and obtain the following useful equations to describe the wave motion: y(x, t) A sin ω(t - x/v) A sin 2Ï€ f(t - x/v)y(x, t) A sin 2Ï€(t/T - x/v)y(x, t) A sin (ω t - kx) The Wave Equation One final feature of the wave function is that applying calculus to take the second derivative yields the wave equation, which is an intriguing and sometimes useful product (which, once again, we will thank the mathematicians for and accept without proving it): d2y / dx2 (1 / v2) d2y / dt2 The second derivative of y with respect to x is equivalent to the second derivative of y with respect to t divided by the wave speed squared. The key usefulness of this equation is that whenever it occurs, we know that the function y acts as a wave with wave speed v and, therefore, the situation can be described using the wave function.

Impact and flexure tests on hampfibre Essay Example | Topics and Well Written Essays - 1000 words

Impact and flexure tests on hampfibre - Essay Example Before analyzing the given data, we must have a look at the basic preliminaries and definitions about the deformation, impact velocity, Hooke’s law and others, Deformation Deformation is the study in continuum mechanics which defines the transformation of an object (material) from its original (reference) shape to a newly adapted form. Deformation can be caused by the external stress (force) effects such as electromagnetic force, gravity, stress, strain and load or temperature. Impact velocity It is the relative measure of the velocity of one object to another in a very small transient time before the interaction of the two objects (interaction could be the result of applied force). In ideal scenario the velocity of the impacting object must not be reduced to 0 and it rarely happens in practical situations. velocity_(impact) = (m_1\vec v_(1f) + m2 vec v_(2f))/m_1 ~ Vec_v shows the velocity vector*. Hooke’s law Hooke’s law is a concept of classical mechanics which discusses the force needed to compress or extend the shape by an amount X (distance). Hooke’s law is also a measure of the deformation of solid bodies as long as deformation impact is small. It is also defined as the first order linear approximation or the material response studied in material science and material engineering (Bansal, 2010). Plastic region: Area under the stress-strain graph after bypassing which, the permanent change and deformation in a material starts occurring. This plastic region is shown in the stress strain graph as the highest point in the curve. Before plastic limit, there is an elastic limit under which the material does not deform itself but it remained confined in the actuality of its originality. However as soon as the elastic and the plastic limit is breached Plastic deformation take place in this deformation, upon uplifting the force and the load, the material does not regain its shape but it tends to adapt the newly deformed shape as the cons equence of the load applied to bring about the change of the shape. Stress: Any force applied in purpose to change the shape and objet and to make that object slide against its own structure. \Shear Stress: It is the force which attempts to deform an object by applying pressure on the surface of the object. Sress = Force/Area (i.e. force per unit area) Stress is not a vector. It is a tensor. Elastic Deformation: region in the stress-strain graph where the deformation take place in a transient mode. It means that the deformation in this region is temporary. Beyond this limit, the material experiences plastic deformation which is permanent. Figure #1 The above figure shows the effect of the impact velocity on the three shapes and different samples. The above figure shows that the impact velocity of the 30 degree conical and the 90 degree conical shape is nearly the same because of having a harmony in the shape (as both are conical). The next shape which is a hemispherical shape, the f igure shows that it has less impact of the relative impact velocity as compared to the rest of the figures. Because the hemisphere has a changed shape and surface as compared to the conical tip, it exhibits an elasto-plastic dynamic behavior under examination. This also relates with the hemispherical heavenly bodies and other cosmological objects who while colliding with each other do not cause any explosion or sudden disruption, but are slowly deformed resulting catastrophic vibration (seismic) activities. Figure # 2 This diagram shows the effect of the load variation and its results on the various samples of three different shapes. With the varying samples of these conical 30, conical 90 and hemispheres shapes the load is also being shown to be varying and gradually rising under the scenario of the change of the shapes. This shows that as the shapes change the ability to deform an object or bypassing its deforming threshold and the requirement of the force to perform this task var ies in accordance with the