DISTANCE x.Taking moment about '0'Kx × 2L = mg × L\(x = \FRAC{{mg}}{{2k}}\)From similar triangle property \(\frac{x}{{2L}} = \frac{\delta }{L}\)\(\delta = \frac{x}{2} = \frac{{mg}}{{4k}}\)Using static DEFLECTION of the mass 'm'\({\omega _n} = \sqrt {\frac{g}{\delta }} = \sqrt {\frac{{4K}}{m}} \)

"> DISTANCE x.Taking moment about '0'Kx × 2L = mg × L\(x = \FRAC{{mg}}{{2k}}\)From similar triangle property \(\frac{x}{{2L}} = \frac{\delta }{L}\)\(\delta = \frac{x}{2} = \frac{{mg}}{{4k}}\)Using static DEFLECTION of the mass 'm'\({\omega _n} = \sqrt {\frac{g}{\delta }} = \sqrt {\frac{{4K}}{m}} \)

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A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is:

Mechanical Vibrations Undamped Free Vibration in Mechanical Vibrations . 6 months ago

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Explanation:Displacing the rod by a small DISTANCE x.Taking moment about '0'Kx × 2L = mg × L\(x = \FRAC{{mg}}{{2k}}\)From similar triangle property \(\frac{x}{{2L}} = \frac{\delta }{L}\)\(\delta = \frac{x}{2} = \frac{{mg}}{{4k}}\)Using static DEFLECTION of the mass 'm'\({\omega _n} = \sqrt {\frac{g}{\delta }} = \sqrt {\frac{{4K}}{m}} \)

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Posted on 16 Nov 2024, this text provides information on Mechanical Vibrations related to Undamped Free Vibration in Mechanical Vibrations. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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