A sinusoidal function is a pur e oscillation like cos or sin or mor e generally cos As you can see the last form includes both of the pr evious two by letting 1 and 0 or 2 In the temperatur e model sinusoidal input could epr esent the diurnal da ID: 28802 Download Pdf

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A sinusoidal function is a pur e oscillation like cos or sin or mor e generally cos As you can see the last form includes both of the pr evious two by letting 1 and 0 or 2 In the temperatur e model sinusoidal input could epr esent the diurnal da

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Exponential Input; Gain and Phase Lag: Introduction The case of sinusoidal input is of gr eat importance in applications. A sinusoidal function is a pur e oscillation like cos or sin , or mor e generally , cos . (As you can see, the last form includes both of the pr evious two by letting 1 and 0 or 2) . In the temperatur e model, sinusoidal input could epr esent the diurnal (day and night) varying of outside temperatur e. In the concentration model it could epr esent the diurnal varying of the level of some hor mone in the bloodstr eam, or the varying concentration in a sewage

line of some waste pr oduct pr oduced periodically by a manufacturing pr ocess. In this session we ar e going to estrict our attention to rst or der con- stant coef ﬁcient ODE’s. Befor e looking at sinusoidal input we will look at exponential input. For constant coef ﬁcient equations we will be able to use the method of optimism to ﬁnd a solution without having to compute integrals. For sinusoidal input, we will use Euler ’s formula to convert si- nusoids to complex exponentials, and so our solutions for exponential input will apply to sinusoids as well.

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