By Janusz Krodkiewski

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**Extra resources for Mechanical Vibration**

**Example text**

50. It can be considered as a rigid body of the mass m and the moment of inertia about axis through its centre of gravity IG . It is supported with by means of the spring of the stiﬀness k and the damper of the damping coeﬃcient c. The motion of the lower end of the spring with respect to the absolute coordinate x can be approximated as follows x = X cos ωt where X stands for the amplitude of the oscillations of the point C and ω stands for the frequency of these oscillations. Produce: 1. the diﬀerential equation of motion of the vibrating table and present it in the standard form 2.

133) Tension in the rope R after the contact of the weight with the floor is lost Without any harm to the generality of the further consideration one may assume that the time corresponding to the instant of separation is equal to 0. For t > 0, the equation of motion of the winch and the block (see Fig. 135) ANALYSIS OF ONE-DEGREE-OF-FREEDOM SYSTEM k 54 c x m x T xb L T Mg Figure 42 Where Lo stands for the initial length of the rope (the lenght the rope had at the instance t = 0). 141) m+M m+M m+M The particular solution of the non-homogeneous equation can be predicted as a constant magnitude A.

4ω n this reaction is smaller then the excitation force and tends to zero when the frequency of excitation approaches infinity. Forced response due to the kinematic excitation - vibration isolation The physical model of a system with the kinematic excitation is shown in Fig. 31b). Motion of the point B along the axis y causes vibration of the block M. This physical ANALYSIS OF ONE-DEGREE-OF-FREEDOM SYSTEM 41 a) b) x M v y G k y c B L a R Figure 31 model can be used to analyze vibration of a bus caused by the roughness of the surface of the road shown in Fig.