Suspension by two vertical parallel fibres, as of a galvanometer needle.
The restitution force is gravity, the torsion being comparatively slight
and negligible. Leaving torsion out of account the restitution force is
(a) proportional to the distance between the threads;. (b) inversely
proportional to their length; (c) proportional to weight of the needle
or other object suspended; (d) proportional to the angle of
Assume two masses A and B at the end of a weightless rod, suspended by
the parallel cords a A, b B. Let the rod be rotated through an angle
theta. Consider the cord a A. Its lower end is swung through the angle
theta, as referred to the center O; the cord is deflected from the
vertical by an angle psi, such that a A tang(psi)= O A 2 sin (theta/2).
The component of gravitation tending to restore A to A, acting towards A
is equal to m g tan(psi). Its moment around O is equal to (m g tan(psi))
* (O A cos(theta/2). The whole moment of the couple is 2 m g
0 A. cos(theta/2) = 2 m g (O A2/ a A) 2 sin(theta/2). Cos(theta/2) =
2mgl(OA2/aA) sin(theta). The moment of the restoring force is thus
proportional to the sine of the angle of deflection, and the
oscillations of such a system are approximately simple harmonic.
If the twisting is carried so far as to cause the threads to cross and
come in contact with each other the suspension ceases to be a bifilar
suspension, but assumes the nature of a torsional suspension.
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