Standard Solutions of the Second-order, Linear, Homogeneous ODE
We are studying the ODE
d2x / d t2
+ 2 α dx / d t
+ ω02x = 0.
Q = ω0 / (2 α) is called the quality factor.
The standard solutions are:
XH(t): Solution with unit height and zero slope
at t = 0.
XS(t): Solution with zero height and unit slope
at t = 0.
The plot shows XH(t) in blue and
a scaled version of XS(t) in orange.
Use the Q slider at the bottom of the page or
click close to the semicircle
or the negative real axis to place the pole on the s-plane.
The other pole will be automatically determined.