Awater tower is idealized as a mass m on top of a uniform and massless beam. the bottom end of the beam is fixed to the ground. the beam has solid circular cross section with a diameter of 1.2 m. its young’s modulus is 30 gpa, and its length is 10 m. the mass m is 20 tons. find the natural frequency and natural period of this system in lateral oscillations.

Natural frequency=21.40 Hz

Time= 0.2936 seconds

Explanation:

Idealizing the question as a cantilever beam with point load of mass M as 20 tons

Lateral stiffness, where l is length given as 10 m, E is Young’s modulus given as 30GPa and I is inertia where for a circular cross-section is given by

k== 9160884.178

k=

To find the frequency, , the mass m is given as 20 tons or 20000 Kg

=21.40196741 Hz

Natural frequency=21.40 Hz

Time period,

T==0.2935798 seconds

T=0.2936 seconds

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e/c, where e is its total energy