what are the factors affecting the stability of amplitude and frequency of oscillators?

Answer 1

Assuming that the oscillator is atleast reasonably designed with relatively hi Q parts the main thing affecting stability is temperature induced variation in parts values. Since an oscillator is basically an amplifier with frequency controlled feedback the variations in value of components will also effect the amplitude.

Answer 2

A simple oscillator (a mass on a spring in a vacuum) has a frequency (in radians per second) determined by the following formula:
omega = sqrt(k / m)
where omega = frequency, k = spring stiffness, and m = mass

This simple system, once started, will oscillate forever without changing. However, when you introduce non-linear effects like friction (spring friction, air resistance, etc.), the amplitude will decay over time, but it is not always apparently exactly how it will do so.

The system can be further complicated if there is both non-linear friction, and an oscillating driving force. If the driving force and friction are great enough, the system can enter a region of chaotic behavior, which is characterized by tiny differences in starting conditions leading to drastic differences later on. This is known as "sensitive dependence on initial conditions".

My apologies if you were referring to a different kind of oscillator.

Answer 3

Another factor in the stability of quartz crystal oscillators is time. An XO's frequency will drift from the time it is first powered up. Indeed parts with tighter stability i.e. 25 ppm or less are actually burned-in or "aged" before they are shipped.

Answer 4

That is not a simple question, but some of the basic factors would be;

Stability of the power supply; does it maintain a constant voltage, are there fluctuations due to other loads, etc.
Quality of the components of the circuit - eg do their values change with temperature, humidity, etc. How do they respond to long-term exposure to extremes of environment.
Control of the environment - temperature, pressure, humidity, acceleration (important for airborne/spaceborne applications).
and many more...