The equation of free vibration of a system is \(\frac{{{d^2}x}}{{d{t^2}}} + 64{\pi ^2}x = 0.\) Its natural frequency would be

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ESE Mechanical 2014 Official Paper - 2

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Answer 1

\(\frac{{{d^2}x}}{{d{t^2}}} + 64{\pi ^2}x = 0\)

\(\Rightarrow \ddot x + 64{\pi ^2}x = 0\)

Comparing this equation with

\(m\ddot x + c\dot x + kx = 0\)

We get, m = 1, k = 64π²

\({f_n} = \frac{1}{{2\pi }}\sqrt {\frac{k}{m}} = \frac{1}{{2\pi }}\sqrt {\frac{{64{\pi ^2}}}{1}} = 4\)