mathematical expressions for both a single pendulum and the coupled pendulum system‚ in particular the equation of motion: Where J is the moment of inertia (=)‚ is the length of the pendula‚ and is the length down the pendulum of the coupling device. If we then use the identity‚ and assume that‚ for small angles‚ we can simplify this equation to: As the coupled pendula system exhibit two modes‚ this equation can be written in two ways: We can then write and as follows‚ by using trigonometric rules:
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Quarter 1 Exam Answer the questions below. Make sure to show your work when applicable. Solve the absolute value equation. Check your solutions. | 5x + 13| = –7 5x + 13 = -7 5x = -20 X = -4 Simplify the expression below. 6n2 - 5n2 + 7n2 6 – 5 + 7 = 8 =8n2 The total cost for 8 bracelets‚ including shipping was $54. The shipping charge was $6. Write an equation that models the cost of each bracelet. 8 x + 6 = 54 $8.00 each bracelets The total cost for 8 bracelets
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Chapter 7: Intro to Sampling Distributions Sampling Error = x̄ - μ Z-Values for a sampling distribution of x̄ : Z = Z-Values adjusted with Finite Population Correction Applied if: the sample is large relative to the population (n is greater than 5% of N) and sampling Is without replacement Z = Using the Sampling Distribution for Means Compute the Sample Mean Define the sampling distribution μx̄ = Define the probability statement of interest P(z30 will give sampling distribution that
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EE2 Signals and Linear Systems Pier Luigi Dragotti Electrical & Electronic Engineering Department Imperial College London URL: http://www.commsp.ee.ic.ac.uk/~pld/Teaching/ E-mail: p.dragotti@imperial.ac.uk PLD Autumn 2012 Thursday‚ 27 September 12 Signals and Linear Systems Lecture 1 Aims and Objectives “The concepts of signals and systems arise in a variety of fields and the techniques associated with these notions play a central role in many areas of science and technology
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Physics Equations and Formulas By Steven Holzner Part of the Physics I For Dummies Cheat Sheet Physics is filled with equations and formulas that deal with angular motion‚ Carnot engines‚ fluids‚ forces‚ moments of inertia‚ linear motion‚ simple harmonic motion‚ thermodynamics‚ and work and energy. Here’s a list of some important physics formulas and equations to keep on hand — arranged by topic — so you don’t have to go searching to find them. Angular motion Equations of angular motion are
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formula 5670 + 2(5670)(.035) + 5670(.035)2 P = $5670 and r = 3.5% = .035 The interest rate with decimals P + 2Pr + Pr2 expanded formula 5670 + 2(5670)(.035) + 5670(.035)2 The expanded equation with values entered 6073.84475 The answer or $6‚073.84 is the rounded answer
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Curve-Fitting Project – Linear Model: Average Sales Prices of new homes sold in the United States between 1964 and 2008 (LR-1) Purpose: To analyze the average sales prices of new homes sold in the United States from 1964 to 2008. Data: The prices were retrieved from http://www.census.gov/const/uspriceann.pdf. I chose to use the prices between 1964 and 2008 as they showed a huge increase (More data was available (see link)). Average sales prices of new homes sold in the US Year Time (seconds)
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Linear Predictive Coding Jeremy Bradbury December 5‚ 2000 0 Outline I. II. Proposal Introduction A. Speech Coding B. Voice Coders C. LPC Overview III. Historical Perspective of Linear Predictive Coding A. B. C. IV. V. VI. History of Speech & Audio Compression History of Speech Synthesis Analysis/Synthesis Techniques Human Speech Production LPC Model LPC Analysis/Encoding A. B. C. D. E. Input speech Voice/Unvoiced Determination Pitch Period Estimation Vocal Tract Filter Transmitting the Parameters
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Band broadening theory (Van Deemter equation) It is well recognized now that column band broadening originates from three main sources: 1. multiple path of an analyte through the column packing; 2. molecular diffusion; 3. effect of mass transfer between phases. In 1956 J.J. Van Deemter introduced the equation which combined all three sources and represented them as the dependence of the theoretical plate height (HETP) on the mobile phase linear velocity. Originally‚ it was introduced for gas
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the case of second-order ODEs‚ such an ODE can be classified as linear or nonlinear. The general form of a linear ODE of order is an(x)dnydxn+an-1(x)dn-1ydxn-1+…+a1(x)dydx+a0xy=f(x) If f(x)is the zero function‚ the equation is said to behomogeneous. Many methods for solving higher order ODEs can be generalized to linear ODEs of ordern‚ where nis greater than 2. If the order of the ODE is not important‚ it is simply called a linear ODE. a). Variation of Parameters Let’s‚ an(x)dnydxn+an-1(x)dn-1ydxn-1+…+a1(x)dydx+a0xy=f(x)
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