Calculate Displacement at Any Frequency: f_modal, d_modal, f_actual

[ncr7]

So I have been trying to figure out how much an object is displaced when subjected to certain frequencies. If I know the modal frequency and max displacement at modal frequency can I find displacement at any frequency?

I was thinking maybe using ratios you could do the following,

modal frequency: f_modal
actual frequency: f_actual
Displacement at modal frequency: d_modal
Displacement at actual frequency: d_actual

d_actual = (f_actual/f_modal)*d_modal

Would this be correct?
The output kind of makes sense I guess...

say if your modal frequency is 2548.67 Hz creates 14.89mm displacement, and you want to know at 15 Hz. Giving a displacement of .08 mm.

 

[nasu]

Quite vague what you are trying to find.
are you talking about a system undergoing forced oscillations? And if this is the case, by f_modal do you mean one of the the resonant frequencies?
If this is the case, the displacement is not proportional to the frequency. The resonance curve is not a straight line. You can approximate it as such for small frequency intervals. But even if you do this, you may have something like

d-d_resonance= A(f-f_resonance),

for a specific small frequency interval.

The proportionality constant depends on where on the curve you do the approximation and how narrow is the resonance curve (which in turn depends on the damping).

If you mean something completely different, never mind. Just give the details.

 

[ncr7]

I guess there would be a function in this case. I am working with inventor simulation studio and it gives a displacement at natural or modal frequencies. Although I am unsure if that data is even correct because inventor maybe giving meaningless data.

Is there a way to analyze displacement if the natural frequency is given?