Respuesta :
Answer:
The dampening constant of the oscillation is 0.00698 kg/s.
Explanation:
Given that,
Frequency = 1.58 Hz
Time = 46.5 s
We need to calculate the dampening constant of the oscillation
Using equation of decay of amplitude
[tex]A=A_{0}e^{\dfrac{-bt}{2m}}[/tex]....(I)
[tex]\dfrac{A}{A_{0}}=\dfrac{44.2}{100}[/tex]
Put the value into the equation (I)
[tex]\dfrac{44.2}{100}=e^{\dfrac{-bt}{2m}}[/tex]
[tex]ln(\dfrac{44.2}{100})=\dfrac{-bt}{2m}[/tex]
[tex]ln(\dfrac{44.2}{100})=\dfrac{-b\times46.5}{2\times199\times10^{-3}}[/tex]
[tex]-b=\dfrac{2\times199\times10^{-3}ln(0.442)}{46.5}[/tex]
[tex]b=0.00698\ kg/s[/tex]
Hence, The dampening constant of the oscillation is 0.00698 kg/s.
