Thanks for the update. I would not say that even 1st and 2nd modes are similar (the shapes are frequencies differ - Analysis 1st frequency is ~ 32% higher). A higher frequency indicates a stiffer structure. Try calibrating your model for 1st mode - try getting the model to have a mode shape similar to the experiment.
Also, another question when you are simulating a wall why constrain it using springs? How did you get the stiffness of the springs? Is the wall constrained using the springs during the experiment?
If you can share an image of the experimental setup then maybe it be easier for members to suggest more on the setup.
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