Can somone explain this review solution (vibrations)?

In summary, the conversation discusses the use of the value 'a' in relating the force generated by a spring to the angle θ and as the lever arm length for the moment about the pivot generated by the spring force. It is also clarified that the negative sign in the equation is due to the assumed direction of the weight and spring force.
  • #1
whitejac
169
0

Homework Statement


Capture.PNG


Homework Equations


The equations are all given

The Attempt at a Solution


This isn't really a homework question... it's solved, but I'm having a hard time following it. I don't understand where the first term:
-a(kaθ)

comes from. I can see it's the moment relation between the hinge and the spring but why is the a term squared?
 
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  • #2
upload_2017-5-1_12-6-29.png
Value 'a' is used to relate the force generated by the spring to the angle θ and as the lever arm length for the moment about the pivot generated by the spring force .
 
Last edited:
  • #3
Nidum said:
View attachment 197634Value 'a' is used to relate the force generated by the spring to the angle θ and as the lever arm length for the moment about the pivot generated by the spring force .
Looking at it again. I'm sorry. I think my problem was just misreading the answer.
Value a just the value used to reference the length? (6in)

This would make:
F spring = xk
x = aθ

Thus a(kaΘ) = M
And it's negative because the fbd assumes the weight is tending CW while the weight and the spring force tend CCW?
 

1. What is the purpose of a review solution for vibrations?

The purpose of a review solution for vibrations is to provide a comprehensive understanding of the underlying principles and concepts related to vibrations. It helps to explain the various components and parameters involved in the study of vibrations and how they affect the behavior of mechanical systems.

2. How does the review solution for vibrations work?

The review solution for vibrations typically involves a combination of theoretical analysis and practical examples. It starts by explaining the fundamental concepts and equations related to vibrations, and then progresses to more complex topics such as forced vibrations and damping. It may also include simulations and real-life case studies to illustrate the application of these concepts.

3. What are some common topics covered in a review solution for vibrations?

Some common topics covered in a review solution for vibrations include free and forced vibrations, natural frequency, resonance, damping, and vibration isolation. It may also cover advanced topics such as modal analysis, Fourier analysis, and vibration control techniques.

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A review solution for vibrations can benefit anyone who is studying or working in the field of mechanical engineering, structural engineering, or any other related field. It can also be helpful for individuals who are interested in learning about the basic principles of vibrations and their applications in various industries.

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A review solution for vibrations can be helpful in practical applications by providing a strong foundation of knowledge and understanding of vibrations. This can aid in the design and analysis of mechanical systems, such as engines, turbines, and structures, to ensure their safe and efficient operation. It can also be useful in troubleshooting vibration-related problems and implementing effective solutions.

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