Maxwell Cohen Table of functions used in ENGR 132 Type of equations General form The plot that shows your data as linear Linear y=mx + Linear Standard graph b Y vs. X Exponential X y=bemx ln(y) =mx+ln(b) Y = mx+B semilogy mx y=b10 log(y) =mx+log(b) log(Y) vs. X Logarithmic* x=bemy ln(x) =my+ln(b) X = my+B semilogx my x=b10 log(x) =my+log(b) Y vs. log(X) Power y=bxm ln(y)=m*ln(x)+ln(b) Y = mX+B log-log log(Y) vs. log(X) *logarithmic equations with calculations done in Excel or MATLAB you will have
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–––– Run ∆y y 2 - y1 ––– = ––––––– ∆x x 2 - x1 1- Solve for y to put the equation in slope intercept form. 2- Plot the y-intercept. 3- Using the slope as a fraction‚ rise y and run x to get second point. 4- Graph the line. Ex: 2x+3y=12 -2x -2x ––––––––– 3y=-2x+12 –– –––– 3 3 y= -2/3x+4 m= -2/3 b= 4 Horizontal and Vertical Lines: - A Horizontal Line has the form y=#. (In an equation of a horizontal line‚ there is no x) - The slope of a horizontal line is 0. Picture:
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mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example 2 Consider the system given by the differential equation y + 4 y + 3 y = 2r (t )‚ where r(t) is the input to
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Aristotle attributed the first of what could be called a scientific discussion on magnetism to Thales of Miletus‚ who lived from about 625 BC to about 545 BC.[1] Around the same time‚ in ancient India‚ the Indian surgeon‚ Sushruta‚ was the first to make use of the magnet for surgical purposes.[2] There is some evidence that the first use of magnetic materials for its properties predates this‚ J. B. Carlson suggests that the Olmec might have used hematite as a magnet earlier than 1000BC[3] [4] In
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Differential Equations 1 2 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS Introduction Differential equations can describe nearly all systems undergoing change. They are ubiquitous is science and engineering as well as economics‚ social science‚ biology‚ business‚ health care‚ etc. Many mathematicians have studied the nature of these equations for hundreds of years and there are many well-developed solution techniques. Often‚ systems described by differential equations are so complex
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Point-Slope Form of the Equation of a Line 9 Section 2.3 Linear Functions and Slopes Write the point-slope form of the equation of the line with slope of 3 that passes through (-1‚2). Substitute into the point-slope form; y-y1 m( x x1 ) y 2 3( x 1) y 2 3( x 1) 10 Section 2.3 Linear Functions and Slopes Solving in Both Forms A. Write the equation in point slope form of the line with slope 4 that passes through the point (4‚-3). B. Then solve the equation for y. x1 y1 y-y1 = m(x-x1)
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was weighed and the mass was measured. Then we calculated the moles of the precipitate. From these calculations‚ we established moles of the limiting reactant‚ were the same amount of moles in the product based on the stoichiometrically balanced equation. Next the percent yield of the limiting reactant was calculated. In Part B of this experiment‚ two solutions were added to the aqueous product in order to determine the limiting reactant. Once each solution was added‚ we were able to visibly see
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CHM 2330 Physical Chemistry Lab Winter 2015 Manual revised 2006 by Maude Boulanger (with Prof. P. Mayer and Prof. D. Bryce) Contact information: Prof. David Bryce dbryce@uottawa.ca -1- TABLE OF CONTENTS Schedule of experiments .......................................................................................................... - 3 General Lab Information ........................................................................................................ - 4 Guidelines for Laboratory
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Straight Lines‚ Pair of Lines & Circles A straight line through the point A 3‚ 4 is such that its intercept between the axes is bisected at A . It’s equation is 1. (a) 4 x 3 y 24 Ans: a (b) 3x 4 y 25 (c) x y 7 (d) 3x 4 y 7 0 Sol: By formula required equation is given by x y 2 4 x 3 y 24 3 4 2. The equation of the line which is the perpendicular bisector of the line joining the points 3‚ 5 and 9‚3 is (a) 4 x 3 y 14 0 Ans: d Sol: A 3‚
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and the rate of deceleration (dec). D=W/g dec (5) With the total amount of drag forces on the aircraft at various angles of attack‚ the coefficient of drag (C_D) can be calculated. This calculation process follows similar equation to the coefficient of lift (C_L) in equation 4; however‚ it includes the force of drag (D) instead of the force of lift (L). The information needed for this calculation was collected from the flight
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