Force Transmitted To the Ground:

Let a machine that is supported by foundation. The foundation may be replaced through a spring and damper. This system is illustrated in Figure 6. As damper and spring are in contact along ground, the force is also transmitted by the damper and spring.

The force transmitted F_t is specified by following

Ft   = k x + c ?

∴             x = X sin (ωt - φ)

∴             ? = X w cos (ωt - φ)

∴             F_t  = k X sin (ωt - φ) + c w X cos (ωt - φ)

Assume        k = R cos α  and      c w = R sin α

∴             tan α= cω/ k

∴             α= tan^-1  cω/ k        --------- (11)

Here α is phase angle among response and force transmitted.

 ∴            F_t  = X R sin {(ωt - φ) + α}        ----------(12)

            ------------------ (13)

Assume

  ----------------(14)

F_T is the amplitude of force transmitted to the ground

∴             F_T    = F_T sin {(ωt - φ) + α}                          --------------- (15)

here

            ------------(16)

F_T is the amplitude of transmitted force and hence, this is the maximum force transmitted.