Derivation of Equations of Resonance

In summary, the group discussed using 3 different types of wine glasses in a vibrations lab experiment to determine resonance. While Wikipedia has the equations for this, they do not explain the derivation behind them. The best way to understand the math behind these equations is to look at the 1D or 2D wave equation and solve it with the specific boundary conditions. Having knowledge of the separation of variables method for solving PDEs would also be beneficial.
  • #1
roldy
237
2
For a vibrations lab experiment, our group decided to determine the resonance of 3 wines glasses, conical, cylindrical, spherical. I know that on Wikipedia they have these equations. What they don't have is how they derived them. I would like to know the math behind these. I've tried searching on the web but to no luck. Is there any place I could find out more or does anyone here know anything about them? Thanks for any help
 
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  • #2

1. What is resonance and how does it occur?

Resonance is the phenomenon in which an object or system vibrates at its natural frequency in response to an external force. It occurs when the frequency of the external force matches the natural frequency of the object or system.

2. How can the equation of resonance be derived?

The equation of resonance can be derived using the principle of superposition, which states that the displacement of a system due to multiple forces is equal to the sum of the individual displacements. By setting up and solving the equations of motion for a damped harmonic oscillator, the equation of resonance can be obtained.

3. What are the factors that affect the resonance frequency?

The resonance frequency of a system is affected by three main factors: the mass of the object, the stiffness of the system, and the damping coefficient. A higher mass or stiffness will result in a lower resonance frequency, while a higher damping coefficient will decrease the resonance amplitude.

4. What are some real-life applications of resonance?

Resonance has many practical applications, such as in musical instruments, where the strings or air columns are designed to vibrate at specific frequencies to produce different notes. It is also used in radio and television receivers, where the resonance of electronic circuits is used to amplify and select specific frequencies.

5. How can resonance be avoided or controlled?

In some cases, resonance can be unwanted and can cause damage to structures or equipment. To avoid or control resonance, engineers use techniques such as changing the mass or stiffness of the system, adding damping materials, or changing the design of the structure to alter the natural frequency and prevent resonance from occurring.

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