Explanation Given Information: The weight ( W A ) of platform A is 100 lb. The spring constant ( k B and k D ) is 120 lb/ft . The load of the block ( P ) of 80 lb. Assume the acceleration due to gravity value is 32.2 ft/s 2 . Calculation: Calculate the equivalent spring constant ( k e ) using the relation: k e = k B + k D Substitute 120 lb/ft for k B and 120 lb/ft for k D . k e = 120 + 120 = 240 lb/ft Calculate the mass of the platform A ( m A ) using the relation: m A = W A g Substitute 100 lb for W A and 32.2 ft/s 2 for g . m A = 100 32.2 = 3.1056 lb ⋅ s 2 /ft Calculate the natural circular frequency ( ω n ) spring using the relation: ω n 2 = k e m A Substitute 240 lb/ft for k e and 3.1056 lb ⋅ s 2 /ft for m A . ω n 2 = 240 3.1056 = 77.28 ( rad/s ) 2 Write the expression for equivalent spring constant ( k e ' ) : k e ' = k B + k D + k C Substitute 120 lb/ft for k B and 120 lb/ft for k D

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Author: BEER

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Chapter 19.1, Problem 19.25P

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The required constant (kC) of spring C.

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The required constant ( k C ) of spring C .

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