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Lateral stiffness of a spring
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From your diagram I would analyze the lateral stiffness in a similar fashion to a beam with one end fixed and the other displaced with with an end moment. See the attached sketch that in my mind would represent your situation. Formulae for beams are found in many strength of material textbooks, steel books and mechanical engineering handbooks. Some type of experimental work will be required on your part to determine the moment of inertia of a flexible beam subject to large deflections since the classical beam formulae are based on very small deflections.
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