Figure Q3 shows an electric motor of total weight of = 8,000 on a simply supported beam. The beam is a rectangular hollow section (RHS) with a span of = 8 and modulus of elasticity of = 200. The electric motor applies a constant force of = 0. sin(), with the amplitude of 100 and circular frequency of 15 /. Assume the weight of the beam in comparison to the electric motor is negligible. For all three sections, clearly show your working and indicate any assumptions made.

a) Calculate the undamped fundamental (circular) natural frequency of free vibration of the beam in bending

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