Slope2

A finite differencing scheme is used to compute the slope. Two values of the signal, one on either side of the point of interest are used as shown in the figure below.

Example

Example

You want to compute the stiffness of a translational nonlinear spring at time T=5 seconds. The spring has an I MARKER=66, a J MARKER=55 and a free length, L0=100 mm.

Here is a code fragment that would perform this calculation.

>>> # Force at T=5.1
>>> y2 = ValueAtTime (
      label         = "Force @ T=5.1",
      measuredValue = "FM(66,55,55)",
      atTime        = 5.1,
      delta         = 1e-1,
    )

>>> # Displacement at T=5.1
>>> x2 = ValueAtTime (
      label         = "Displacement @ T=5.1",
      measuredValue = "DM(66,55,55)",
      atTime        = 5.1,
      delta         = 1e-1,
    )

>>> # Force at T=4.9
>>> y1 = ValueAtTime (
      label         = "Force @ T=4.9",
      measuredValue = "FM(66,55,55)",
      atTime        = 4.9,
      delta         = 1e-1,
    )

>>> # Displacement at T=4.9
>>> x1 = ValueAtTime (
      label         = "Displacement @ T=4.9",
      measuredValue = "DM(66,55,55)",
      atTime        = 4.9,
      delta         = 1e-1,
    )

>>> # The Slope at T=5.0
>>> k5 = Slope2 (
      label = "Slope@5", 
      points = (y2,x2,y1,x1),
    )

The calculation in Slope2 for this example is implemented as:(1)

k 5 = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}