The natural frequency of vibration for small displacements, Mechanical Engineering

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The natural frequency of vibration for small displacements

In the Hartnell governor shown in Fig. 2.71, the stiffness of the spring is N/m and the weight of each ball is 25 N. The length of the ball arm is 20 cm, and that of the sleeve arm is 12 cm. The distance between the axis of rotation and the pivot of the bell crank lever is 16 cm. The spring is compressed by 1 cm when the ball arm is vertical. Find

(a) the speed of the governor at which the ball arm remains vertical and

(b) the natural frequency of vibration for small displacements about the vertical position of the ball arms.

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Mechanical Engineering: The natural frequency of vibration for small displacements

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