Statics and Dynamics Quiz
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A water tower is idealized as a lumped mass MM atop a massless elastic column of lateral stiffness kk. The tower undergoes undamped free lateral vibration. An engineer proposes to lower the natural frequency by 50% (i.e., achieve ωn,new=0.5 ωn,old\omega_{n,new} = 0.5\,\omega_{n,old}) to avoid resonance with a nearby excitation source.
If only the mass MM can be modified (the column stiffness is fixed), by what factor must MM be multiplied to achieve the desired reduction in natural frequency?
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