T1-22 Hz. When the machine is installed on five linear isolators with rubber flexible elements selected in accordance with the manufacturer's recommendations, different for different mounting points (line 2, fn = 15 Hz), the maximum amplitude of the relative vibrations (resulting in waviness of the ground surface) was 0.35 3m. However, when the grinder was installed on five  indentical  CNF  isolators  with  rubber  flexible  elements  (line  1,  fn  =  20  Hz,  or  about  two  times  stiffer  than  the  linear isolators), the maximum relative vibration amplitudes was 0.25 3m, about 30% lower. 7.0    CONNECTIONS OF SPRING ELEMENTS 7.1    Springs in Parallel These combine like electrical resistance in series. This is the case when several springs support a single load, as shown in Figure 34. The springs are equivalent to a single spring, the spring constant of which is equal to the sum of the spring constants of the constituent springs. The spring constant k of the single equivalent spring is given by: k = k1 + k1 + k1.                                                                                                           (27) 7.2    Springs in Series The series connected springs in Figure 35 combine like electrical resistances in parallel. The equivalent single spring is softer than any of the component springs. The spring con- stant k of the equivalent single spring is given by:             =       +       .                                                                                                            (28) If n springs are in series, this formula is readily extended to:             =       +       +       + ..... +        .                                                                               (29) 7.3    Spring Connected Partly in Parallel and Partly in Series Obtain equivalent spring constants for each set of parallel or series springs separately and then combine. For example, in Figure 36, the springs k1 and k2 are equivalent to a single spring, the spring constant of which, ke1, is given by:               =       +       =                        or        ke1 =                                                           (30a) The three springs, k3, k4, k5 in parallel, are equivalent to a single spring, the spring constant of which, ke2, is given by: ke2 = k3 + k4 + k5                                                                                                      (30b) Now equivalent springs ke1 and ke2 are in series. Hence, the spring constant k of the equiva- lent spring for the entire system is:             =         +               or        k =                                                                                 (30c) 0.5 0.2 0.25 0.35 0.1 0.05 10 15 Frequency (Hz) 20 25 30 1 2 35 Figure 33    Amplitude of Relative Motion in Work Zone with:  1 - Regular (Linear) Isolators; 2 - CNF Isolators 1 __ k 1 __ k1 1 __ k2 1 __ k 1 __ k1 1 __ k2 1 __ k3 1 __ kn 1 ___ ke1 1 __ k1 1 __ k2 k1 + k2 _______ k1k2 k1k2 ______ k1 + k2 1 __ k 1 ___ ke1 1 ___ ke2 (k1k2)(k3 + k4 + k5) ______________________ k1k2 + (k1 + k2)(k3 + k4+ k5) k1 k2 k1 k2 k3 Figure 34    Parallel                     Connection                     of Springs Figure 35    Series                     Connection                     of Springs k1 k2 k3 k4 k5 Figure 36    Mixed                     Connection                     of Springs