3-Lesson_Notes_Lecture17_ee205 - Lecture 17 The following...

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Lecture 17 The following topics are covered in this lecture A damped sinusoid Special cases of damped sinusoid Example with damped sinusoidal input Comparison with sinusoidal excitation RLC circuit representation for damped sinusoidal excitation A Damped Sinusoid Consider the damped sinusoid function () cos( ) t m vt V e t σ ω θ =+ (19-1) Plot of the function is given in the following figure t m Ve m V v t Figure 19-1. A damped Sinusoid Function In the figure above, V m is the peak value of the damped sinusoid, ω is the angular frequency (radian) of oscillation, θ is the shift (leading) of
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the cosine function, and σ (sigma) is a real quantity usually negative. Although we refer to this function as being “damped”, it is possible that the sinusoidal amplitude may increase if σ is positive. From sinusoidal analysis we already know the radian frequency ( ω ) or frequency f in Hz. We will see later σ is also part of frequency, called real part of complex frequency. σ is also called the Neper frequency. Special Cases Let us now investigate some special cases of the damped sinusoid given by equation (19-1). Case 1 : σ =0 The equation (19-1) becomes a general sinusoidal voltage with a phase shift θ , () cos( ) m vt V t ω θ =+ (19-2) m V v t Figure 19-2. Special case of a damped Sinusoid Function for s=0
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Case 2 : ω =0 Equation (19-1) now represents an exponential function () cos( ) t m vt V e σ θ = t m Ve = (19-3) Sketch of this function is given in Fig.19-3 t V
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This note was uploaded on 01/16/2010 for the course EE ee205 taught by Professor Profsyed during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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3-Lesson_Notes_Lecture17_ee205 - Lecture 17 The following...

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