I've come across some notation that I've never had to deal with, so I'm not to sure what I'm supposed to do.

I have an equation $\displaystyle s(t) = e^{-\frac {t}{2}}cos(2t)$

I'm supposed to show by direct substitution that the displacement satisfies the differential equation

$\displaystyle 4\frac{d^2s}{dt^2} + f\frac{ds}{dt} + 17s = 0$

I'm really thrown off by the term 'direct substitution' as we haven't used it in this unit. What am I supposed to substitute into what??

Also, the notation of $\displaystyle \frac {d^2s}{dt^2} $ is confusing me too - what is this in relation to?

Also, please, no giving me answers to the equation, I'm moreso after an explanation of what I'm supposed to be doing here...