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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Calculation of spring stiffness and time of complete swing for two different mass-spring system configurations.

Identifier  ExFiles\Box 43\2\  Scan195
Date  28th September 1937 guessed
  
Case I
DEFLECTION UNDER LOAD.
SPRING STIFFNESS (RATING) = W/d
TIME OF COMPLETE SWING
= 2π * sqrt(disp / acc) = 2π * sqrt(x / ((W*x/d) / (W/g))) = 2π * sqrt(d/g)

Case II
DEFLECTION UNDER LOAD.
SPRING STIFFNESS (RATING) = W / 2d
TIME OF COMPLETE SWING
= 2π * sqrt(disp / acc) = 2π * sqrt(x / (Wx/2d)) [struck through]
= 2π * sqrt((x/2) / ((Wx/d) / (W/g))) = 2π * sqrt(d / 2g)
i.e. TIME = .707 of time in Case I
  
  


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