Consider this equation of a damped harmonic oscillator such that: $$ \ddot{x}+2\gamma\dot{x}+\omega^2_0=0 $$
with: $\gamma=\frac{b}{2m}$ and $\omega_0=\sqrt{\frac{k}{m}}$
Finally, we know that the equation x(t) should be of this form: $$ x(t)=e^{-\gamma t}[Acos(\omega_1t)+Bsin(\omega_1t)] $$
It is observed that the amplitude of oscillation of a tuning fork of frequency 400Hz is damped in the air by 10% in 12s. What would be the frequency of the tuning fork in a vacuum (void)?
I'm really struggling to find a starting point… I've found that: $$ \omega_1=\frac{\sqrt{4mk-b^2}}{2m} $$ But I don't see where to begin to find the frequency in the vacuum. Could someone explain me how to start?
Thank you in advance.