Two Discs on a Rod - Solving Normal Freqs & Modes

In summary, the conversation discusses a problem involving two discs of equal mass and radius, supported along a slender rod and attached at their centers. The goal is to calculate the normal frequencies and normal modes of the system. The person has calculated the kinetic and potential energy equations and is unsure if they are correct. They also ask for a hint on how to find the time it takes for disc 1 to have all the kinetic energy.
  • #1
Feynmanfan
129
0
Dear friends,

I'm having trouble with this problem, I don't know if I'm doing it right, I'd be grateful if you could advice me.

Two discs, each of mass M and radius R, are supported with equal
separation along a slender rod to which they are rigidly fastened at
their centers as shown in the picture I attached below.

I need to calculate the normal frequencies and normal modes.

This is what I've done:

T(kinetic energy)=1/2*1/2MR^2(theta1^2+theta2^2)
V(potential)=1/2*k(theta1^2+theta2^2+(theta1-theta2)^2

Where theta is the angle the disc turns. Does this make sense?

THanks!
 

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  • #2
well,

If what mentioned above is right, I found out that either in phase or counterphase are the system's normal modes.

The thing is that, at the beginning both discs start from 0 but disc number 2 has an initial velocity u. I am asked to describe the motion and calculate how long it will take the first disc to get all KINETIC ENERGY.

Don't solve the problem for me, but just give me a hint what I should do.

THanks
 
  • #3
is it possible that disc 1 can receive all the kinetic energy?
 
  • #4
please. I need help
 

FAQ: Two Discs on a Rod - Solving Normal Freqs & Modes

1. What is the purpose of solving normal frequencies and modes for two discs on a rod?

Solving normal frequencies and modes for two discs on a rod allows us to determine the natural oscillations and vibrations of the system. This information is helpful in understanding the behavior of the system and can be used to design and improve structures and machines.

2. How do you calculate the normal frequencies and modes for two discs on a rod?

The normal frequencies and modes can be calculated using mathematical equations and principles, such as the Euler-Bernoulli beam theory and the Rayleigh method. These methods involve determining the stiffness and mass of the system and then solving for the natural frequencies and corresponding modes.

3. What factors can affect the normal frequencies and modes of two discs on a rod?

The normal frequencies and modes of two discs on a rod can be affected by various factors, such as the stiffness and mass of the discs and rod, the length and diameter of the rod, and the boundary conditions. Any changes in these factors can alter the natural frequencies and modes of the system.

4. How does solving normal frequencies and modes help in practical applications?

Solving normal frequencies and modes can help in practical applications by providing insight into the dynamic behavior of the system. This information can be used to optimize the design of structures and machines, improve their performance, and avoid potential issues such as resonance and fatigue failure.

5. Can the normal frequencies and modes of two discs on a rod be experimentally determined?

Yes, the normal frequencies and modes of two discs on a rod can be experimentally determined using vibration testing techniques. This involves exciting the system at different frequencies and measuring the response to determine the natural frequencies and modes. These experimental results can be compared to the calculated values for validation.

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