Find Natural Frequency $\omega_n$
Using this formula for the percentage overshoot, the damping ratio is given by

$$\zeta=\sqrt{\frac{\log(0.4)^2}{\pi^2+\log(0.4)^2}}=0.28$$

which is more or less the same value that you obtained. Consequently, you have an underdamped system. The peak frequency $\omega_{max}$ of the frequency response is related to the damping ratio and to the natural frequency in the following way (link):

$$\omega_{max}=\omega_n\sqrt{1-2\zeta^2}$$

With $\zeta=0.28$ and $f_{max}=500\text{ Hz}$ this results in a natural frequency $f_n=544.51\text{ Hz}$. Apart from a scaling factor, a second order system is completely characterized by $\zeta$ and $\omega_n=2\pi f_n$.