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Titlebook: Linear vibrations; A theoretical treatm P. C. Müller,W. O. Schiehlen Book 1985 Springer Science+Business Media Dordrecht 1985 kinematics.mu

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Free vibrations are obtained for the nongyroscopic conservative vibrating systems. Here it also becomes visible that the amplitudes of natural modes decrease with increasing natural frequencies. Moreover, the natural modes for weakly damped and ordinary mechanical systems will be presented.
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Matrix equationsThree types of linear algebraic equations are of importance in the treatment of linear vibrating systems: the linear vector equation . the Ljapunov matrix equation . and Stein’s matrix equation . One section will subsequently be devoted to each of these.
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State equations of linear vibrating systemsf motion can be transformed into the ., i.e. into a first order differential equation for the state vector of the system. Ordinary mechanical vibrating systems and the analogous electrical systems may be equally represented by their equations of motion or their state equations. This is however not t
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