Valve Driving Force

With these areas and the corresponding geometric couplet defined, the motion of the valve opening $x(t)$ is governed by

$$m\frac{d^2x}{dt^2} + 2m\gamma\frac{dx}{dt} + k(x-x_0) = \sigma_1 p_1 (S_1+S_3) + \sigma_2 p_2 S_2,$$

where $\gamma$ is the damping coefficient, $x_0$ the equilibrium position of the valve opening in the absence of flow, $K$ the valve stiffness, and $m$ the reed mass.

The couplet therefore, is very useful when evaluating the force driving a mode of the vibrating valve.