Content of the report

Laboratory work № 4-6

I. Homework

(answer the control questions from p.28).

II. Laboratory work № 4-6 implementation protocol.

1) Topic:

EXPLORING of FORCED OSCILLATIONS in SERIES RLC-CIRCUIT.

2) Goal: 1. Studying of effective value of voltage on capacitor and effective value of current dependencies in the series RLC-circuit versus ratio of driven frequency to the circuit’s eigenfrequency.

2. Studying resonance phenomena in AC RLC-circuit.

3) Scheme of laboratory research facility:

V – voltmeter; C – capacitor; R – resistor; L – inductor (coil); ГЗ-36 – AC generator;

4) Table of measuring instruments:

5) Equations for calculation:

1. Generator cyclic frequency:

Ω_GEN = 2πν_GEN,

where ν_GEN – generator linear frequency in Hz.

2. Amplitude of current in the circuit:

I_m = 2π·ν_GEN·C·U_C Ö2,

where C – capacity of a circuit (one of the set), U_C – effective voltage on capacitor.

3. Quality factor of the circuit:

,

where U_C^RES – effective voltage on capacitor at resonance; U_GEN – effective driving EMF (ГЗ-36 output voltage, determined by Г3-36 voltmeter scale).

4. Inductance of the circuit:

,

where Ω_RES – resonance frequency.

5. Resistance of the circuit:

.

6) Table of measurements

C= … F; U_GEN = … V.

7) Quantities calculation:

Q = … ;

L = … mHn;

R = … Ohm.

8) Graphs of U_C(Ω) and I(Ω) dependencies:

9) Final results :

1. Q = … ;

2. L = … mHn;

3. Ω_RES = … kHz;

4. R = … Ohm.

10) Conclusion:

Work done by: Work checked by:

WORK 5-1

EXPLORING OF STANDING WAVES VIA MELDE METHOD

Goal of the work

1. Studying parametric resonance phenomena.

2. Studying conditions of standing waves generation.

3. Determination of vibrator oscillations frequency.

Main concepts

Waves.

A wave is a propagation of oscillations in space. Oscillations of elastic medium cause elastic waves, oscillations of electric and magnetic fields – electromagnetic waves. An oscillating mechanism that is a source of waves is called vibrator.

Elastic waveis the mechanical disturbance (deformation) of a medium propagates through that medium. Propagation of elastic waves is in excitation of oscillations of more and more remote points of a medium. Set of oscillating points of given medium is called thewave field.Oscillation of each point is forced by vibrator (or another points). A locus of points having the same phase is called thewave surface. The wave front is a wave surface whith maximal distance from source at present moment. With respect to the shape of wave front there are traveling waves, plane waves, spherical waves.

In longitudinal waves the points of medium oscillate at parallel to the direction of propagation. This type of waves related with compressive deformation of medium and able to propagate in solids, liquids, and gaseous mediums. In transverse waves the points of medium oscillate at perpendicular to the direction of propagation. These waves can only occur in media that oppose to shear deformation. Only solids have such property. That is why transverse waves propagate only in solids.

The phase velocityof a wave is physical quantity which numerically equal to distance at which any point of wave surface travels by unit of time. Vector of phase velocity points in the direction of wave propagation, perpendicularly to wave surface. The wavelength of a sinusoidal wave is a distance between any two next points with the same phase. From another standpoint, wavelengthis a distance which any phase of wave transits for a period.

,

(65)

where – period of a wave (smallest time interval after which the value of oscillating quantity is being repeated), f – frequency of a wave (number of oscillations per unit time), k – the wavenumber (number of wavelengths per 2π distance).

Each point of one-dimensional traveling wave oscillates according the waveequation (equation of traveling wave in differential view)

,

(66)

General solution for this differential equation (66) will be equation of traveling wave

Date: 2015-12-24; view: 788