The Space Needle observation tower can be considered as a cantilever beam that is fixed at the ground (Figure 3). Find an idealized spring-mass system equation of the observation tower and determine the natural frequency. *[Hints: For the study of transverse vibration, the top mass can be considered a point mass, and the supporting structure (beam) can be approximated as a spring to obtain the single-degree-of-freedom model. The transverse deflection of the beam, due to a load F, is given by FL³/3EI]***Figure 3. Space Needle observation tower in Seattle, Washington.**Explanation:The image shows the Space Needle observation tower, which is located in Seattle, Washington. The tower is used as an example to illustrate the concept of modeling a structure as a cantilever beam for studying transverse vibrations. In this context, the tower's supporting structure is likened to a spring in a single-degree-of-freedom system. The equation provided offers insights into calculating the deflection of the beam under a load using the parameters F (force), L (length), E (modulus of elasticity), and I (moment of inertia).

Given data: Let space needle observation tower be taken as a cantilever beam To determine: Idealised…

The space needle observation tower can be considered as a cantilever beam that is fixed at the ground (Figure 3). Find an idealized spring-mass system equation of the observation tower and determine the natural frequency. [Hints: For the study of transverse vibration, the top mass can be considered a point mass, and the supporting structure (beam) can be approximated as a spring to obtain the single-degree-of-freedom model. The transverse deflection of the beam, due to a load F is given by FL/3EI]

The space needle observation tower can be considered as a cantilever beam that is fixed at the ground (Figure 3). Find an idealized spring-mass system equation of the observation tower and determine the natural frequency. [Hints: For the study of transverse vibration, the top mass can be considered a point mass, and the supporting structure (beam) can be approximated as a spring to obtain the single-degree-of-freedom model. The transverse deflection of the beam, due to a load F is given by FL/3EI]

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

The Space Needle observation tower can be considered as a cantilever beam that is fixed at the ground (Figure 3). Find an idealized spring-mass system equation of the observation tower and determine the natural frequency.

*[Hints: For the study of transverse vibration, the top mass can be considered a point mass, and the supporting structure (beam) can be approximated as a spring to obtain the single-degree-of-freedom model. The transverse deflection of the beam, due to a load F, is given by FL³/3EI]*

**Figure 3. Space Needle observation tower in Seattle, Washington.**

Explanation:
The image shows the Space Needle observation tower, which is located in Seattle, Washington. The tower is used as an example to illustrate the concept of modeling a structure as a cantilever beam for studying transverse vibrations. In this context, the tower's supporting structure is likened to a spring in a single-degree-of-freedom system. The equation provided offers insights into calculating the deflection of the beam under a load using the parameters F (force), L (length), E (modulus of elasticity), and I (moment of inertia).

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