Detuner stiffness

The steady state response of a spring/mass system with viscous damping when excited by the abutment can be shown to be,

With no damping we have,

With no dampng the force amplitude (F) on the abutment because of the motion is given by

The 'Dynamic" stiffness at the abutment is given by the force amplitude (F) divided by the displacement amplitude Xo,

It is apparent that the dynamic stiffness is infinite when,

which is when the excitation frequency,