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Expressing in terms of $\textrm{w}_\textrm{1}, \textrm{w}_\textrm{eff}$ <br><math> \sin^2\theta \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) = \frac{w_\textrm{1}^2}{w_\textrm{eff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right) = Figure ==\frac{w_\textrm{See Figure 1}^2}{w_\textrm{1}^2 + \Omega^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right)</math>and 10 in the reference:
== Figure ==See Figure 1 and 10 in the reference. Palmer, A.G. & Massi, F. (2006). Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem. Rev. 106, 1700-1719 [http* {{#lst://dx.doi.org/10.1021/cr04042875 DOI]Citations|PalmerMassi06}}
→Figure: Switched to labelled section transclusions for the citation.
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== Equation ==
<math>
\mathrm{R}_{1\rho}= \mathrm{R}_1\cos^2\theta + \left( \mathrm{R}_{1\rho}{´} + \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) \sin^2\theta
</math>
Expressing in terms of {{:omega1}}, {{:omegaeff}} <br>
<math>
\sin^2\theta \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) =
\frac{w_\textrm{1}^2}{w_\textrm{eff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right) =
\frac{w_\textrm{1}^2}{w_\textrm{1}^2 + \Omega^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right)
</math>
== Ramp code ==
<source lang="python">
plt.figure(1)
plt.plot(data[:,2], data[:,3], '.')
plt.ylabel(r'Imaginary Rex, ramping spin-lock field strength, nu1')
plt.xlabel(r'Rotating frame tilt angle')
Omega = np.arange(0., 20, 1)
plt.figure(2)
plt.plot(data[:,2], data[:,3], '.')
plt.ylabel(r'Imaginary Rex, ramping spin-lock offset')
plt.xlabel(r'Rotating frame tilt angle')
plt.show()
</source>
== Equation = Ramping ===<math>[[File:ramp_w1_ramping_spin-lock_field_strength.png|thumb|center|upright=2|Ramping spin-lock field strength : w1]]\mathrm{R}_{1\rho}[[File:ramp_Omega_spin-lock_offset.png|thumb|center|upright= \mathrm{R}_1\cos^2\theta + \left( \mathrm{R}_{1\rho}{´} + \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) \sin^2\theta </math>|Ramping spin-lock offset : Omega]]
[[File:Fig1 Palmer Massi 2006.png|thumb|center|upright=3|Try to reproduce Figure 1.]]
Figure produced with script [[Relax_disp.spin_lock_offset%2Bfield_figure | found here. ]]
== See also ==
[[Category:Relaxation_dispersion analysis]]
