A scissors jack is used to lift a load \(W\). The links of the jack are rigid and the collars can slide freely on the shaft against the springs of stiffnesses \(k_{1}\) and \(k_{2}\) (see Fig. 2.63). Find the natural frequency of vibration of the weight in the vertical direction.

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Collar W Shaft Link Collar FIGURE 2.63 Weight lifted by scissors jack. k