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An experiment conducted over time T necessarily produces a windowed view of the phenomenon generating the data. It is a useful strategy to regard the windowed data as one period of a periodic function. Then one may write
and seek to calculate the Fourier coefficients cn from the integral expression
Large values of cn will be regarded as a quantitative indication of a genuine periodic change in the phenomenon under study. In digital form the relevant equations are
The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
Define a mapping from the x,y plane to the u,v plane by u = 2x + y, v = -x +2y . If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 de
Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl
I. The inventory of records of BeBop Distributing reflected the following for October 2012: Date Transaction Units
prove that A=3i+j-2k ,B= -i+3j+4k, C=4i-2j-6k can form a triangle and find the length of the medians of the triangle.
As an engineering student, the ministry of energy and minerals has tasked you to help them model equation(s) that can estimate the amount of crude oil in a reservoir. The governmen
A stone weighing 50 newton is tied to one end of a cord 0.90 meter long. the stone is then whirled in a vertical circle. if the breaking strength of the cord in tension is 60 newto
a wire of 3mm diameter and 5 m long has a load of 100g suddenly applied to its ends. calculate stress and extension produced. also show that these are twice the static values
A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds
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A scientist calculates the temperature of melting platinum using a new type of thermometer. The temperature of the metal is called to be exactly 1768.3 centigrade. The measurements
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