Question
Consider, The motion of a a damped harmonic oscillator is described by x′′
x
″
b
x
′
k
x
=
0
, where b is greater than or equal to 0
ARewrite as a two dimensional linear system.
x′=y
x
′
=
y
y′
y
′
= - (by+kx)
(
b
y
+
k
x
)
BSketch the analogue of the trace-determinant plane in the bk-plane. That is, identify the regions in the relevant portion of the bk-plane where the corresponding system has similar phase portraits.
I have cut out most of my answer etc as it seems to of merely confused people, how does one answer this question?
