Here <https://en.wikipedia.org/wiki/Harmonic_oscillator> we have an equation for displacement of a mass on a string as a function of time.

${\displaystyle x(t)=A\cos \left({\sqrt {\frac {k}{m}}}t\right)}$

In the same wikipedia article it is mentioned a few times that a dampened spring-mass "system" can exponentially decay.

How is the above equation augmented to account for dampening? 

It is simply by multiplying by $e^{-\lambda t}$?

If yes, how do we interpret/define our $\lambda$?