Answer
given,
mass of the boiled egg = 50 g = 0.05 Kg
spring constant, k = 25 N/m
initial Amplitude, A₁ = 0.3 m
final amplitude, A₂ = 0.1 m
time, t = 5 s
considering the amplitude of damped harmonic oscillation to calculate damping factor.
![A_2 = A_1 e^{-(\dfrac{b}{2m})t}](https://tex.z-dn.net/?f=A_2%20%3D%20A_1%20e%5E%7B-%28%5Cdfrac%7Bb%7D%7B2m%7D%29t%7D)
b is the damping factor and t is the time.
![e^{-(\dfrac{b}{2m})t}=\dfrac{A_2}{A_1}](https://tex.z-dn.net/?f=e%5E%7B-%28%5Cdfrac%7Bb%7D%7B2m%7D%29t%7D%3D%5Cdfrac%7BA_2%7D%7BA_1%7D)
on solving
![b= \dfrac{2m}{t}ln(\dfrac{A_1}{A_2})](https://tex.z-dn.net/?f=b%3D%20%5Cdfrac%7B2m%7D%7Bt%7Dln%28%5Cdfrac%7BA_1%7D%7BA_2%7D%29)
inserting all the given values
![b= \dfrac{2\times 0.05}{5}ln(\dfrac{0.3}{0.1})](https://tex.z-dn.net/?f=b%3D%20%5Cdfrac%7B2%5Ctimes%200.05%7D%7B5%7Dln%28%5Cdfrac%7B0.3%7D%7B0.1%7D%29)
b = 0.0219 Kg/s
damping coefficient in three significant figure
b = 0.022 Kg/s