Spring-Driven Mass

To keep the model physical, let's use a pre-compressed spring as our force-source for driving the mass:

Physical Diagram

Equivalent Circuit

• The mass and spring form a loop, so the connection can be defined as either parallel or series (as determined by the element reference directions)

• We arbitrarily choose a parallel junction, giving the following physical constraints:
  • $f_k(n)=f_m(n)$ (common force)
  • $v_k(n)+v_m(n)=0$ (sum of spring-compression-velocity and rightgoing-mass velocity is zero)
• Exercise: Work out the case for a series junction and verify everything comes out the same physically
• Connecting our wave digital spring and mass at a parallel force-wave junction is depicted as follows:

WDF Diagram

Note the WDF symbol ``$\vert\vert$ '' for a parallel adaptor (scattering junction)