UTT MATH1002 Weeks 3&4 Notes Systems of ODEs First-order linear equations with constant coefficients [pic] [pic] Let [pic] [pic] Taking Laplace transforms of (1) and (2) [pic] [pic] From (3) and (4) [pic] [pic] We solve this system algebraically for [pic]and [pic] and obtain [pic] by taking inverse transforms. Example [pic] [pic] [pic] We have [pic] [pic] [pic] From (5) and (6) [pic] [pic] [pic]
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Project Specifications Project Title: Variable Pitch Constant Rotational Speed Wind Turbine Project Aims This project can be divided into 3 three parts. The first part is to develop a variable pitch propeller. Then second and the main aim of this project is to design a control mechanism by which the propellers would rotate at a constant speed‚ at varying wind speeds by adjusting their pitch. This would be achieved by using wind sensors (anemometer) and a microcontroller. The sensors would
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Coefficient of Friction- Post Lab Abstract The purpose of the experiment was to determine to coefficient of friction on a block sliding across a horizontal plane‚ and on the same block sliding down an inclined plane. This was done by first testing block‚ and how much weight on a string was needed to move the block at a constant velocity using a pulley system. The block weighed 0.2385 kilograms‚ and needed a hanging mass of 0.05 kg to move at a constant velocity. This means the coefficient of
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class. Show your work. 1. Match the differential equation in (a)-(c) to a family of solutions in (d)-(f). The point of this exercise is not to solve the differential equations in a) - c). (a) y = y 2 (b) y = 1 + y 2 (c) yy = 3x (d) y = tan(x + C) (e) 3x2 − y 2 = C (f) y = −1/(x + C) 2. Find the value of k so that y = e3t + ke2t is a solution of y − 2y − 3y = 3e2t . 3. Solve the following differential equations and IVP’s. You may solve these equations implicitly. (a) y + 3x2 y = x2 (b) y ln t = y+1
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DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH‚ 2nd Edition DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA‚ Gian Paulo A. ECE / 3‚ Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves
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Measuring the Absorption Coefficient for Some Common Materials Used in Functional Rooms through Standing Wave Ratio Adonis Cabigon1‚ Alaiza Tangaha2 Department of Physics‚ University of San Carlos‚ Nasipit‚ Talamban‚ Cebu City 6000 1adoniscc@yahoo.com 2mayalaiza92@yahoo.com Abstract In this paper‚ we present the measurement of the absorption coefficient α of MDF (Medium Density Fiberboard) and Fiber Cement through an improvised standing wave apparatus consist of an enclosed tube with
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Coefficient of variation Sample-> CY=s/x 1. A relative measure of dispersion 2. Adjusts for differences in magnitudes of the means. 3. Does not have units of measure 4. Allows for direct comparisons of mean-adjusted dispersion across different data sets. Percentiles and quartiles Coefficient of determination The proportion of variation in the dependent variable ”explained” by the independent variable. 因變量的變化的比例“解釋”的獨立變量。 (Correlation coefficient)^2=r^2 R=0.90 (0
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Laboratory Coefficients of Friction Discussion: Friction is the force that resists motion and can be determined in either static situations or kinetic situations using the following equation: [pic] Static friction is the amount of friction that resists the start of motion and kinetic friction resists an object’s continued motion. The coefficient of friction depends on a number of factors including surface area and the types of surfaces in contact. The only way to determine a coefficient of friction
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Significance of the Value Equation for Global Marketers According to Keegan (2002)‚ the value equation can be considered as a guide to create perceived value for customers by any organization operating anywhere in the world. The value equation is known as V=B/P‚ where V is the value‚ B is benefits and P is price. The value can be increased in two ways‚ by increasing the numerator ‘benefits’ or by reducing the denominator ‘price’. Keegan (2002) elaborates that the benefits can be increased by
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intensity is half its maximum ■ To find the points where the pattern achieves its half-power (-3 dB points)‚ relative to the maximum value of the pattern: o Field pattern at 0.707 value of its maximum. o Power pattern (in linear scale) at its 0.5 value of its maximum. o Power pattern (in dB) at -3 dB value of its maximum. [pic][pic] iii) ▪ First-null beamwidth (FNBW) is the angle between two vectors‚ originating at the
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