The static deflection x_ st = F_0/k is used to express the natural frequency as:

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Mechanical Engineering QUESTION #2451

Question 1

The static deflection \(x_{st} = F_0/k\) is used to express the natural frequency as:

\(\omega_n = \sqrt{g/x_{st}}\) (using gravity \(g\) and static deflection under weight)✔️
\(\omega_n = x_{st}/g\)
\(\omega_n = k\cdot x_{st}\)
\(\omega_n = g\cdot x_{st}\)

Correct Answer Explanation

Since \(x_{st}=mg/k\), we have \(k/m=g/x_{st}\), hence \(\omega_n=\sqrt{k/m}=\sqrt{g/x_{st}}\).