# How to scale x-axis with a parameter which scals y axis as well while ploting?

x = ComplexExpand[(ωm^2 - ω^2 - I*ω*γm - (G^2*δ*ωm)/((k - I*ω)^2 + δ^2))]

k = 0.2
δ = 10
G = 0.3
γm = 0.000001
ωm = 10

Plot[(Abs[(Re[x] + ω^2)^(1/2)]/ωm), (ω, -20,20},
AxesLabel  -> (HoldForm[ω/ωm], HoldForm[ωeff1/ωm]),
LabelStyle -> (GrayLevel[0], Bold),
PlotStyle  -> (Thick, Green),
PlotRange  -> All]


I want to scale on both axis with $$\omega_{m}$$ y axis is scaled but not x-axis. While scaling with $$\{\omega/\omega_{m}, -10,10\}$$ in the above plot for x-axis, it shows some iteration error.

I tried with $$\Omega$$= Range[-10,10]; t = $$\Omega/\Omega_{m}$$ and it shows strange behavior along y-axis.

How can I scale x-axis with $$\Omega/\Omega_{m}$$?

• You cannot use List brackets (curly braces) as if they were parentheses. See The Four Kinds of Bracketing in the Wolfram Language. You have not provided a definition for the parameter a Commented Nov 5, 2019 at 21:16
• Depending on how you want to scale the x-axis, you need to do one of the following: Scale the limits of $\Omega$: {Ω,-10Ωm, 10Ωm}. Replace Ω with Ω/Ωm during the computation of your function - the easiest is probably to use Block[{Ω=Ω/Ωm}, Abs[...]] Commented Nov 5, 2019 at 21:16
• @Bob I removed those braces and 'a' was a typo there Commented Nov 5, 2019 at 22:22
• @Lukas thanks, scaling while computation worked for me rather than in plotting. Commented Nov 5, 2019 at 22:42

Plot[(Abs[(Re[x] + ω^2)^(1/2)] /. ω -> ω1 ωm)/ωm,

• Just divide to ωm`.