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You are describing a guided cantilever whose deflection y is

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y = PL^3/ (12 EI) where I = wt^3/12

K = P/y = Ew t^3/L^3

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Q: How do you proof that k is equal to Ewttt over lll when k is spring constant E is young's modulus w is width t is thickness and l is lenght?
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