Question

1. Oscillating system performs damped oscillations with frequency 1000 Hz. Determine the frequency of natural oscillations if the resonance frequency is 998 Hz. 2. Amplitude of vibrations during 5 minutes decreased by 2 times, during which time the amplitude reduced by 8 times? 3. For 8 minutes amplitude decreased 8 times. Find damping factor. 4. Determine how much resonance frequency is different from the natural oscillation frequency (1kHz) when the damping factor is 400 s decreased 20 times 6. The amplitude of oscillations is reduced by 10 s from 10 cm to 9 cm. Period of oscillation is 0.4 s. Find damping factor. 7. During the 10 s amplitude decreased 3 times. How long it will decrease by 10 times? 8. What is the frequency of oscillation, if the shortest distance between points in the same phases is I m. Wave propagation speed is 300 m/s 9. Find the wavelength if the rate of spread of 300 m/s, and the period is 0.5 sec.

Answer 1

8.

$\lambda$ = wavelength = 1 m

v = wave propagation speed = 300 m/s

f = frequency of oscillation = ?

frequency of oscillation is given as

f = v/$\lambda$

inserting the values

f = 300/1

f = 300 Hz

9.

v = rate of spread = 300 m/s

T = Time period = 0.5 sec

$\lambda$ = wavelength = ?

wavelength is given as

$\lambda$ = v T

inserting the values

$\lambda$ = (300) (0.5)

$\lambda$ = 150 m