Deteriming resonant frequencies

In summary, the conversation is about converting a function T(s) to T(iω) in order to plot it and find the resonant frequency. The function T(iω) is 7/(ωi*(ω^2+6iω+58)) and in order to find the resonant frequency, the circuit response must be entirely imaginary. Some suggestions have been made on how to solve this, but the speaker is still having trouble. They are seeking additional help or suggestions.
  • #1
mpm
82
0
I am stumped on how exactly to do this.

I have the function: T(s) = 7/s(s^2+6s+58)

I need to change this to T(iω) and i being a complex root.

This creates: T(iω) = 7/(ωi*(ω^2+6iω+58))

I know I need to plot this function and find out where omega peaks and this will be my resonant frequence.

My only problem is I don't know how to plot this.

I've got a TI-89, Excel, or MATLAB if anyone knows how to do this in either of those.

Please let me know.

Mike
 
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  • #2
The circuit will be resonant if there are no real losses. In order for there to be no real losses, the circuit response must be entirely imaginary. Do some algebra to separate the real and imaginary parts, then equivalate the real par to zero. Then try solving it.
 
  • #3
For some reason, I still can't get anything to come out of what you suggested. I understand what you are saying but its just not working.

Anyone have other comments that might help?

Mike
 

What is a resonant frequency?

A resonant frequency is the natural frequency at which an object vibrates most easily. This frequency is determined by the physical properties of the object, such as its size, shape, and material.

How do you determine the resonant frequency of an object?

To determine the resonant frequency of an object, you can use a variety of methods such as mathematical calculations, experimental measurements, or computer simulations. The exact method used will depend on the specific characteristics of the object and the available resources.

Why is it important to determine the resonant frequency of an object?

Determining the resonant frequency of an object is important in various fields such as engineering, physics, and music. It allows us to understand and predict the behavior of vibrating systems, design structures that can withstand specific frequencies, and create musical instruments that produce desired sounds.

What factors can affect the resonant frequency of an object?

The resonant frequency of an object can be affected by several factors, including its physical properties, such as mass and stiffness, as well as external factors such as temperature and humidity. Additionally, the presence of other objects or materials in the surrounding environment can also impact the resonant frequency.

How can you use knowledge of resonant frequencies in practical applications?

The knowledge of resonant frequencies can be applied in various practical ways, such as designing bridges and buildings that can withstand specific vibrations, creating musical instruments with desired tones, and developing medical devices that use resonance for imaging or treatment purposes. It can also be used in troubleshooting and diagnosing issues in mechanical systems that involve vibrations.

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