1. **State the problem:** Given the formula $$f_n = \frac{1}{2 \pi} \sqrt{\frac{g_n}{\delta_{st}}}$$, calculate $f_n$ for specific values of $g_n$ and $\delta_{st}$. 2. **Formula explanation:** This formula calculates $f_n$ as the frequency or a related quantity depending on $g_n$ and $\delta_{st}$. The term $2\pi$ is a constant, and the square root involves the ratio $\frac{g_n}{\delta_{st}}$. 3. **Example 1:** Calculate $f_n$ when $g_n = 9.8$ and $\delta_{st} = 1$. $$f_n = \frac{1}{2 \pi} \sqrt{\frac{9.8}{1}} = \frac{1}{2 \pi} \sqrt{9.8}$$ $$= \frac{1}{2 \pi} \times 3.1305 = \frac{3.1305}{6.2832} = 0.498$$ 4. **Example 2:** Calculate $f_n$ when $g_n = 16$ and $\delta_{st} = 4$. $$f_n = \frac{1}{2 \pi} \sqrt{\frac{16}{4}} = \frac{1}{2 \pi} \sqrt{4}$$ $$= \frac{1}{2 \pi} \times 2 = \frac{2}{6.2832} = 0.318$$ 5. **Example 3:** Calculate $f_n$ when $g_n = 25$ and $\delta_{st} = 9$. $$f_n = \frac{1}{2 \pi} \sqrt{\frac{25}{9}} = \frac{1}{2 \pi} \sqrt{2.7777}$$ $$= \frac{1}{2 \pi} \times 1.6667 = \frac{1.6667}{6.2832} = 0.265$$ These examples show how to substitute values into the formula and simplify step-by-step to find $f_n$.