Description of laboratory research facility and methodology of measurements

There is a vibrator fixed at the edge of laboratory desktop – a rod forced to oscillate by electromagnet. This electromagnet supplied by sinusoidal current, so, the forced oscillations of the rod are driven with frequency of the alternating current. On the opposite edge of the desktop there is a light pulley with a fixed axis of rotation. The vibrator and the pulley joined by a thread. One end of this thread is tied up to vibrator and the other one, thrown through the pulley, is pulled by the load in the plate (see Setup schematic diagram).

In order to determine vibrator frequency we’ll need to obtain stable standing waves pattern. Such pattern might appear only when the condition of parametric resonance matched, i.e. when the vibrator frequency is double one of the natural frequencies of the thread. In this case length of thread l will contain integer number of standing wavelengths λ_st.

Natural frequency of thread’s oscillations depends on its tension. If at some tension of a thread vibrator frequency f_υ is double the lowest frequency f (fundamental harmonic) of the thread, then one standing wave will lay on its length. By decreasing the tension we can obtain conditions at which f_υ is double the second, third,.., n-th harmonic of the thread (frequencies multiple to fundamental harmonic): f_υ =2 f_n. Thus we’ll have 2, 3,…, n standing waves, lying on a thread’s length l.

l = n λst or l = n .

(75)

Relation between thread’s frequency f and λ is so

f = ,

(76)

here υ – velocity of wave propagation in the thread.

The velocity of wave propagation depends on magnitude of tension F, caused by immovable weight, linear density ρ (depends on thread’s mass m) and length l. As , then, including (75) and (76 ) we’ll have

.

(77)

Tension F is caused by the weight of load, so

here M – mass of the load (including mass of a plate). As the vibrator frequency is double thread’s natural frequency, from (78) we’ll have

.

(79)

4 Data processing (see laboratory work № 4-1).

Date: 2015-12-24; view: 596