Force Driving a Mass

Suppose now that we wish to drive the mass along a frictionless surface using a variable force $f(n)$. This is similar to the previous example, except that we now want the traveling-wave components of the force on the mass to sum to $f(n)$ instead of 0:

$$f(n) = f^{{+}}(n) + f^{{-}}(n)$$

Since $f(n)$ and $f^{{-}}(n)$ are given, $f^{{+}}(n)$ must be computed as $f^{{+}}(n) = f(n) - f^{{-}}(n)$. This is shown in Fig.P.8.

Figure P.8: Wave digital mass driven by external force $f(n)$.

The simplified form in Fig.P.8b can be interpreted as a wave digital spring with applied force $f(n)$ delivered from an infinite source impedance. That is, when the applied force goes to zero, the termination remains rigid at the current displacement.