Experimental equipment

Oscillographic method of oscillatory circuit parameters determination

The purpose of the work: to study experimentally and theoretically damped oscillations characteristics of electric oscillatory circuit. To get skills to work with oscillograph.

Experimental equipment

Fig. 1

Principal scheme of electric setting for investigation of free damped oscillations in an oscillatory circuit in this work is represented in Fig. 1. It consists of a source of alternating voltage (step-down transformer of 12 V), experimental bench with diode D (for creation of oscillating process), two capacitors (S₁ and S₂), two inductance coils (L₁ and L₂) and two switches (K₁ and K₂), resistances box and oscillograph.

The scheme (fig. 1) involves two oscillatory circuits with different parameters. Voltage oscillations are given by both oscillatory circuits in turn to the oscillograph with the help of switches K₁ and K₂.

Graph of voltage damped oscillations in the capacitor U = U(t) is obtained on oscillograph screen. A value of circuit resistance (that is damping degree) is chosen by the resistances box and the most convenient values for parameters measurement are set in the first oscillatory circuit (variant 1), and then in the second one (variant 2).

Measurement procedure

1. Complete an electric circuit according to the scheme, represented in fig. 1.

2. Determine the initial amplitude A₁ and the third — fifth amplitudes A_{1 + n} (n = 2, 3, 4) of damped oscilla­tions using oscillograph grid.

3. Determine the oscillation period on the horizontal scale of oscillograph.

Enter the obtained results into table 1. They must have no less than three signs after decimal comma.

Table 1

4. Calculate logarithmic damping decrement d.

5. Calculate damping coefficient b.

6. Calculate own time of the oscillating system.

7. Determine the parameters of two oscillatory circuits.

I variant

Having known value of R (R = R₁ + R₂) calculate L₁ and C₁ according to the formulae:

and .

Fig. 2

where R₁ resistance of bridge MVU-48, and R₂ of a coil.

II variant

Having known value of C₂ calculate L₂ and R₂ according to the formulae:

and .

8. Plot the graph of damped oscillations (Fig. 2) according to the picture on the screen of the oscillograph.

Determine the absolute error of measurement of damping logarithmic decrement according to the formula:

,

where is instrumental error of amplitude measurement = 0,1 cm.

questions to be admitted for doing laboratory work and its defence

1. Differential equation of free damped oscillations of the linear system and its solution (pendu­lum, oscillatory circuit).

2. Basic characteristics of damped oscillations, their physical meaning and measurement units.

3. What is the quality factor of an oscillating system? What is the relationship between damping logarithmic decrement and circuit parameters?

4. Write down expressions for determination of parameters of electric circuit L, C, R.

5. What quantities are determined due to direct and indirect measurement in a given work?

6. How do electric, magnetic and total energies change with time at oscillating in a circuit?

7. At what oscillations addition does trajectory of resulting oscillation get form of ellipse; circle; line?

8. Own electric oscillations.

9. Damped electric oscillations.

10. Energy of electric oscillations.

11. Addition of electric oscillations.

Date: 2015-01-12; view: 1055