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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
the solution of diffusion equation by using separation of variables
r u there?
In closed system 0.3kg of gas at 373K is expanded isothermally and reversibly from 1 mpa pressure to 200 kp. Given that cv= 718 j/kg k and R= 287 j/kgk.
application of mathematics in engineering
An electronic module is mounted on a machine and is modelled as a single degree of freedom spring, mass, and damper. During normal operation, the module of mass m kg is subject to
Evaluate the expression below for various smoothers, plot and compare the results, making appropriate comments.
The following are 8 data points that shows the relationship between the number of fishermen and the amount of fish they can catch a day. (Let the number of fishermen be X and the a
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
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The vertical motion of a general aviation airplane subjected to a sharp-edged wind gust is described by the equation Δw(t) = A g (1-e -t/τ ) assume A g = 30 where Δ w is in
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