Aah thanks guys! Should have spotted that...
So physically the two terms account for the amplitude and the phase?
What about the overdamped case?
x(t)=Ae^{r_{-}t}+Be^{r_{+}t}
with
r_{\pm}=\frac{1}{2}-\beta\pm\sqrt{\beta^{2}-4\omega_{0}^{2}}
Does the fact that the expression...
I was hoping that someone could explain why these different equations can be found from different sources please.
The time dependent position, x(t), of an underdamped harmonic oscillator is given by:
x(t)=e^{-\gamma t}acos(\omega_{1}t-\alpha)
where \gamma is the damping coefficient, and...