of the load being conveyed; wet, amorphous or plastic
pulps seem to apply more damping than inelastic solids
in unit or bulk dry granular form. The damping effect
results from friction losses associated with the work
expended in lifting the load during each cycle, slippage
of the load on the conveying surface, and, in the case
of dry granular materials, interparticle friction.
The interaction of the impressed force, inertia force,
spring force, and damping force is illustrated in the
vector diagrams of Fig. 4.2 For the vibrating system
to be in equilibrium at any frequency ratio, the vector
sum must be zero on any axis.
The diagram in Fig. 4(a) represents the equilibrium
condition at frequency ratios less than unity. Because
the spring force is greater than the inertia force, the
excess must be opposed by the impressed force, which
also must oppose the damping force, with a component
at right angles to the inertia force.
In Fig. 4(b), the frequency of the impressed force
has increased to match the natural frequency of the
spring-mass system. The spring force now equals the
inertia force, and the impressed force has only to oppose
the damping force.