Natural vibration - energy method

In summary, natural vibration is a periodic motion of an object or system without any external intervention. It differs from forced vibration, which is a response to an external force. The energy method is used to determine the natural frequency of an object or system in natural vibration, and it can be harmful to structures if the frequency matches the natural frequency of the structure. The energy method is commonly used in engineering and physics to analyze natural frequencies in practical applications to prevent potential damage.
  • #1
luznyr
28
0

Homework Statement



the problem is in the attached file, I am having trouble with part d and e. cheers. [the answer for B is mr^2(0.5-16/9pi^2)]

Homework Equations





The Attempt at a Solution



i won't upload all my working as i have stuff everywhere but for part d:

i got my answer as 0.5I*(omega^2) + 0.5*m*(r*theta^2+(4r/3pi)^2), using the formula for total kinetic energy as 0.5Iomega^2+0.5mv^2

and part e: mgR(theta.sintheta + costheta - 1)

are these along the right tracks?
 

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  • #2
are you sure your question 3 is correct?
 
  • #3
im not too sure what you mean question three sorry, if by part C, then I'm not too concerned about that for the moment, just part D and E
 
  • #4
sorry... i mean D
 
  • #5
i have no idea if either of my answers for d or e are right, hence why i stuck it on here...im just so confused haha
 

FAQ: Natural vibration - energy method

What is natural vibration?

Natural vibration refers to the periodic motion of an object or system in response to an external force. It is also known as free vibration, as it occurs without any external intervention.

How is natural vibration different from forced vibration?

Natural vibration occurs without any external force, while forced vibration is a response to an external force. Natural vibration is also a characteristic of the object or system, while forced vibration is not.

What is the energy method used for in natural vibration?

The energy method is used to determine the natural frequency of an object or system in natural vibration. It involves calculating the potential and kinetic energy of the object and setting them equal to each other to find the natural frequency.

Can natural vibration be harmful to structures?

In some cases, natural vibration can be harmful to structures if the frequency of the vibration matches the natural frequency of the structure. This can cause resonance and lead to structural damage.

How is the energy method used in practical applications?

The energy method is commonly used in engineering and physics to analyze the natural frequencies of structures and systems, such as bridges, buildings, and vehicles. It helps engineers and designers ensure that the natural frequencies of their designs do not match any external forces, preventing potential damage.

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