Damped Oscillations:

The oscillations shown in figure 1 are known as damped oscillations. Obviously, the electrical system in which such oscillations are produced has electrical (I²R) losses and some energy is lost during each oscillation. Further, no compensating ar­rangement for the electrical losses is provided and as a result, the amplitude of the oscillation reduced to zero. However, the frequency or time period, which is determined by the circuit parameters, remains unchanged.

Damped and Umdamped Oscillations

Undamped Oscillations:

For obtaining constant amplitude oscillations, known as undamped oscillations, as shown in fig .2, exponential term e^_Rt/2L must become unity i.e. value of R, the dissipation component in the circuit must become zero. With R positive, the amplitude decreases with time t while with R negative, amplitude goes on increasing with time t.

In any physical circuit, R is a positive quantity and, therefore, a negative resistance is required to be included so as to neutralize the effect of positive resistance R and thus provide undamped oscillations. Alternatively the undamped oscillations can be obtained if right amount of energy is supplied to overcome the losses at the right time in each cycle. The resulting “undamped oscillations” are called the sustained oscillations. Such sustained oscillations or continuous waves are required to be produced by the electronic oscillator circuits.