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Showing 201 - 210 of 297 results for "The wave"
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https://sheffield.ac.uk/media/32024/download?attachmentc) Reformulating givesdy. dx= (7 3x) 1. ywhich is in the required form. ... Key Point 1. Method of Separation of Variables. The solution of the equationdy. ... Example 3Use the method of separation of variables to solve the differential equation....
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https://sheffield.ac.uk/media/32025/download?attachmentdt2+ R. di. dt+. 1. Ci = 0. Hence write down the complementary function. ... 3. Find the complementary function of the equationd2y. dx2+. dy. dx+ y = 0. ... d2y. dx2= A cos xB sin x. Substitution into the differential equation gives:. ... Example...
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https://sheffield.ac.uk/media/32023/download?attachmentdy. dx= 2x. On integrating, we obtain the general solution. y = x2 C. ... b) Here the second condition is y(1) = 5 so at x = 1. ... Example 2Classify the differential equations specifying the order and type (linear/non-linear). ... Sketch the curves...
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https://sheffield.ac.uk/media/32034/download?attachmentMost of the results obtained are tabulated at the end of the Section. ... This restriction is not too significant in elementary applications of the z-transform. ... cos x =eix eix. 2. we can state, using the linearity property, that. ... Recall now...
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https://sheffield.ac.uk/media/32030/download?attachmentLet us find the solution of. dy. dt+ 2y = 12e3t y(0) = 3. ... d) Draw a graph of the oscillations for t = 0 to 10 s. ... s. (b) Since the system starts from rest x(0) = x′(0) = 0. ... c) Taking the Laplace Transform of each term of the...
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https://sheffield.ac.uk/media/32032/download?attachmentIt is the system that changes the input signal into the output signal. ... 70 HELM (2008):Workbook 20: The Laplace Transform. Engineering Example 3. System response. ... $. %. PrerequisitesBefore starting this Section you should. • be able to use...
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https://sheffield.ac.uk/media/32036/download?attachmenttransfer function of the discrete system. It is often denoted by H(z). ... At zero initial conditions, Y (z) = Y1(z) so the transfer function is. ... We write down the transfer function of (5), using positive powers of z. ... Hence, taking inverse...
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https://sheffield.ac.uk/media/32056/download?attachmentIn effect, thereal variable x is simply replaced by the complex variable zzz. ... 3. Where is f(z) =z. z2 9discontinuous? Find the lim. zif(z). ... A neighbourhood of z0 is the region contained within some circle |xz0| = r.). ... 3. f(z) is...
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https://sheffield.ac.uk/media/32058/download?attachmentz = 0. On each branch the function ln z is analytic with derivative1. ... Then, from the secondrelation: cos y = 1 so k must be an odd integer. ... Each branch is defined on the whole zplane with the exception of the point. ... be familiar with the...
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https://sheffield.ac.uk/media/32062/download?attachmentPrerequisites. Before starting this Section you should. • thoroughly understand the various techniquesof integration. • ... b) The force on an area subjected to constant pressure is given by. ... area of each face of the slice isgiven by the...