How can I plot this amplification diagram?

Question

Levente Kis 2020-4-24

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编辑： Raunak Gupta 2020-4-27

I have to plot the amplification diagram of a nonlinear mechanical system which has harmonic excitation. The amplitude of the system can be calculated by solving the following equation:

where μ and ω are known system parameters, A is the amplitude of the system,

is a proportional parameter to the amplitude of the harmonic excitation, Ω is the angular frequency of the harmonic excitation.

I have to plot the amplification diagram, which means I have to plot this equation on the

plane (Yes, A is between absolute value brackets).

How can I do that.

is arbitrary positive.

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Levente Kis 2020-4-26

I find a way to plot it, but it works only, if I give numeric value to

.

My question is that can I plot it without giving numeric value to

, so can I plot it parametrically?

darova 2020-4-26

you can plot a few graphs or create surface. can't plot without numbers

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Answer 1

Raunak Gupta 2020-4-27

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编辑：Raunak Gupta 2020-4-27

Hi,

As per my understanding you are trying to plot two variables Ω and |A| based on the fo value that you want to give parametrically. Since you want to visualize it as a diagram there need to be a limit placed on Ω and A for plotting.

Similarly, I assume fo is independent of Ω and A so instead of giving a single value of fo to plot I suggest plotting it in a specific range using fimplicit3. In this you may define the given equation which have three variables (Ω, A and fo) and mention the interval in which you want to plot.

As darova pointed in the comments that even if fo is parametric, for showing the equation on a graph it requires some values so that different curve can be visualized for fo values.

Hope it helps.