The Bell has a mass of 385 kg, a center of mass at G, and a radius of gyration a

Question

The Bell has a mass of 385 kg, a center of mass at G, and a radius of gyration about point D of kD = 0.45m. The tongue consists of a slender rod attached to the inside of the bell at C. if an 9kg mass is attached to the end of the rod, determine the length L of the rod so that the bell will "ring silent," i. e., so that the natural period of vibration of the tongue is the same as that of the bell. For the calculation, neglect the small distance between C and D and neglect the mass of the rod.

L = __________

Explanation / Answer

the time period is

T = 2pi x (L/g)

where g = 9.8 m/s^2

Also,

w = (k/m)^1/2

or (2pi/T) = (k/m)^1/2

or T = 2pi x (m/k)^1/2

from the above two equations we have

2pi x (m/k)^1/2 = 2pi x (L/g)^1/2

or L = (m/k) x g

where m = 9 kg and k is spring constant of rod

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