Torsion Spring-mass System

The main features of this device are shown in Fig. 3.9a. The z-axis is directed along the field (the vertical), and the lever with a small mass m rotates around a horizontal axes, passing through the point 0. The length of the lever is a. The torsion spring is installed on the axis, and its torsion constant is equal fi. This is a coefficient of proportionality between the moment t and the rotation angle or. 

Also suppose that the spring has pre-tension moment  

Ftere a is the angle between the vertical and lever. The second moment is caused by weight and its magnitude is equal to product of the lever length and the projection 

Equilibrium takes place when the magnitudes of both moments are equal  

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Fig. 3.9. (a) Torsion mass- spring system, (b-d) function r(a), (e) resultant moment as a function of the angle. 

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