## A vector approach to oscillations |

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accordance with Eq actance diagram actance vector algebraic function amplitude analytically angle contours angular frequency angular velocity behavior clockwise angle complex numbers contour map shown contracted notation cosh counterclockwise angle counterclockwise direction cross section defined by Eq denotes described equiangular spiral exponential function expression factor fixed vectors function F(s given by Eq graphically illustrate the process illustrated in Fig Illustrating calculation indicated in Fig magnitude and direction magnitude contours nepers obtain partial fraction analysis plane pole at position polynominal function position vector quadrature axis quadrature components Quadrature direction reference and quadrature reference axis reference component reference direction represented resultant vector right-hand side rotating vectors saddle point scalar algebra scalar quantity Show shown in Fig side of Eq sinh sinusoidal oscillation Sketch a contour spiraling vector square root terrain time-varying vector unit vector variable vector addition vector algebra vector diagram vector F vector function vector given vector st