A steel bar 25 mm wide and 50 mm deep is simply supported at two points 3 m apart and carries three loads of 1000 N, 1500 N and 750 N at 1 m, 2 m and 2.5 m from the left support. The Young's modulus for steel is 200 GPa. If the mass of the bar is 262 kg/m, find the frequency of transverse vibration.

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Q: - 20 kN/m

A: solution of above problem is below:

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.