Self - Tuning

The most dominant or the primary exciting frequency of a multicylinder engine is given by

, where  for two stroke cycle and    for a two stroke cycle	(17.1)

= number of cylinders, and = rotational speed of the engine, neglecting all the higher harmonics of the system.
Now, the natural frequency of a gravity pendulum of length "" is , where is the acceleration due to gravity.

Figure 17.1: Simple pendulum

If the pendulum moves in a horizontal plane with its hinge point O' (Fig. 17.1)) rotating at a speed with radius , then the gravity field () is replaced by the centrifugal field ( ). The natural frequency  () of this centrifugal pendulum becomes

	(17.2)

Comparing Eqns. (17.1) and (17.2), we see that the necessary condition for self-tuning is

Torsional vibration of crankshaft has been controlled in industrial applications by using a secondary mass in the form of a loose flywheel which is coupled to the vibrating shaft by

1. pendulum damper
2. coulomb friction ( Lanchester damper)
3. viscous fluid friction (Houdaille damper)