Question:
Show that the general relationships between the two initial values of position, x(0),
and velocity, v(0), and the amplitude 
and phase angle 
of Eq.6,
are
and
,
Solution:
We have that 
and after taking first derivative
wrt time, we find 
. Evaluating both
expressions at time t=0, gives
and
.
Therefore, we have that by dividing one
expression by the other.
Further, we use the fact that 
, to write
,
from which it follows that
.