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Free oscillations

Circuits with high frequency oscillations are important parts of all radio transmitters and receivers. In order to understand the operation of such oscillatory circuits we shall analyse the operation of a pendulum. If we pull such a pendulum to one side and then release it, it will oscillate. The oscillations of the pendulum are free oscillations. The movement of the pendulum from the first position to the second position and back is one complete oscillation. After the first oscillation comes the second, third etc. The movement of the pendulum from the first position to the second position does not make one complete oscillation but only half of it.

The maximum deflection of the pendulum from the zero position, i.e. distance 0-1 or 0—2 is the amplitude of oscillations.

The time necessary for the pendulum to complete one oscillation is the period.

The number of oscillations per second is the frequency. They measure the period in seconds, the frequency in cycles (cps), kilocycles (kc), and megacycles (mc).

The oscillations of the pendulum have the following properties:

  1. They damp, i. e. their amplitude constantly decreases as a result of energy losses.

  2. Free oscillations have harmonic character, i. e. they are sinusoidal.

  3. The frequency of free oscillations of the pendulum depends upon its length and does not depend (is independent) of the amplitude.

As the damping process continues the amplitude of oscillations decreases but the period and frequency are constant. As the pendulum oscillates the potential mechanical energy becomes the kinetic one. In position one or two when the pendulum stops, it has the greatest potential energy, while the kinetic energy is equal to zero at that moment. As the pendulum moves from position one or two to zero, the speed of its travel and the kinetic energy (the energy of motion) increase. When the pendulum passes through the zero position its speed and the kinetic energy are the greatest, while its potential energy is equal to zero. After the zero point the pendulum speed begins to decrease and the kinetic energy begins its conversion into the potential one.

EXERCISES

I. Answer the following questions:

1. Where do we use circuits with high frequency oscillations? 2. What is it necessary to do in order to understand the operation of oscillatory circuits? 3. What oscillations has the pendulum? 4. What is one complete oscillation? 5. What is half of one complete oscillation? 6. What is the amplitude of oscillations? 7. What is the period? 8. What do we call the frequency? 9. In what units do we measure the period (frequency)? 10. What are the properties of oscillations? 11. Why does the amplitude of oscillations of the pendulum decrease? 12. Are free oscillations sinusoidal? 13. What does the frequency of oscillations of the pendulum depend upon? 14. Do the period and the frequency of oscillations change? 15. In what position is the potential energy the greatest? 16. When is the kinetic energy equal to zero? 17. When does the kinetic energy begin to convert into the potential one?