How to find the transfer function (frequency response function) given the EOM

In summary, to find the transfer function of a given spring/damper system, you need to find the displacement x(t)/input y(t) by assuming a harmonic forcing function and solving for x(t) using the given equation of motion. Then, replace X0sin(wt-phi) with x(t) and solve for the left side of the equation in terms of x(t). This will give you the frequency response function (FRF), which can be calculated by hand for a single degree of freedom system. You can refer to a standard vibrations book for more information.
  • #1
mattattack900
3
0
for a given spring/damper system the equation of motion is:

[PLAIN]http://img600.imageshack.us/img600/2140/equation1.png [Broken]

where x is the displacement of a mass from a fixed point
d is a damping constant
L1 and L2 constant lengths
k1 and k2 are 2 spring constants
and Y(t) is a harmonic input fuction

How can i find the transfer function of this system?
 
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  • #2
Hi,

You need to find x(t)/y(t). For this you can assume a harmonic forcing function, for example:

Y(t) = Y0 sin(wt)

and corresponding displacement function:

X(t) = X0 sin(wt-phi), where phi is the phase lag between applied force and resultant displacement.

You input these equations in your equation and solve (considering differential xdot and xdotdot). After substitution, replace X0sin(wt-phi) term with x(t).

Then you will get left side of the equation in terms of x(t). x/y gives you FRF.

Being a single dof, it should be easier for you to calculate by hand.

You can refer any standard vibrations book for this.

Best wishes
Geoff
 

1. What is a transfer function and why is it important?

A transfer function is a mathematical representation of the relationship between the input and output of a system. In the context of engineering and science, it is often used to describe the behavior of a system in response to different inputs, such as frequency or time. It is important because it allows us to analyze and design systems, and understand how they will respond to different inputs.

2. How do you find the transfer function given the equation of motion (EOM)?

The transfer function can be found by taking the Laplace transform of the EOM. This converts the EOM from the time domain to the frequency domain, where the transfer function can be easily calculated. The transfer function is then the ratio of the Laplace transform of the output to the Laplace transform of the input.

3. What is the relationship between the transfer function and the frequency response function?

The frequency response function is the magnitude and phase response of the system to a sinusoidal input at different frequencies. The transfer function is the mathematical representation of this relationship. In other words, the frequency response function is the output of the system when the input is a sinusoidal signal at a specific frequency, while the transfer function describes the system's overall response to all possible input frequencies.

4. What information can be obtained from the transfer function?

The transfer function can provide important information about a system, such as its stability, damping, and resonance frequencies. It can also be used to design controllers or filters for the system, and to predict its response to different inputs.

5. Are there any limitations to using the transfer function?

While the transfer function is a powerful tool for analyzing systems, it does have some limitations. It assumes linearity and time-invariance of the system, meaning that the system's behavior does not change over time or with varying inputs. It also may not accurately describe systems with highly nonlinear or chaotic behavior.

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