Mechanical Engineering - Theory of machines - Discussion

Thanks @Anil.

Tan φ=2$r/(1-r^2)^2,
As r=1, φ=90,
As φ=90, from vector diagram the exciting force equals damping force.

Types of vibration.

FREE AND FORCED VIBRATION:

If a system, after an internal disturbance, is left to vibrate on its own, the ensuing vibration is known as free vibration. No external force acts on the system. The oscillation of the simple pendulum is an example of free vibration. If a system is subjected to an external force (often, a repeating type of force) , the resulting vibration is known as forced vibration. The oscillation that arises in machineries such as diesel engines is an example of forced vibration. If the frequency of the external force coincides with one of the natural frequencies of the system, a condition known as resonance occurs, and the system undergoes dangerously large oscillations. Failures of such structures as buildings, bridges, turbines and airplane have been associated with the occurrence of resonance.

UNDAMPED AND DAMPED VIBRATION:

If no energy is lost or dissipated in friction or other resistance during oscillation, the vibration is known as un damped vibration. If any energy lost in this way, however, it is called damped vibration. In many physical systems, the amount of damping is so small that it can be disregarded for most engineering purposes. However, consideration of damping system near resonance.

LINEAR AND NONLINEAR VIBRATION:

If all the basic components of a vibratory system the spring, the mass and the damper behave linearly, the resulting vibration is known as linear vibration. If however, any of the basic components behave non linearly, the vibration is called non-linear vibration.

An impressed force or active force or Newton second law force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line.

How? What is impressed force?