Question 124: Oscillations

Question

A damped harmonic oscillator has a frequency
of 5 oscillations per second. The amplitude
drops to half its value for every 10 oscillations.
The time it will take to drop to
1/1000 of the original amplitude is close to :-

Accepted Answer

Time for 10 oscillations = $${{10} \over 5} = 2\,s$$
A = A
0
e
Ã¢ÂÂkt
$${1 \over 2} = {e^{ - 2k}} \Rightarrow \ln 2 = 2k$$
10
Ã¢ÂÂ3
= e
Ã¢ÂÂkt
$$ \Rightarrow $$ 3In10 = kt
$$t = {{3\ln 10} \over k} = {{3\ln 10} \over {\ln 2}} 	imes 2$$
= $$6 	imes {{2.3} \over {0.69}} \approx 20\,s$$

Answer

100 s

Answer

10 s

Answer

20 s

Answer

50 s

Oscillations

A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to 1/1000 of the original amplitude is close to :-

Choose the correct answer: