1. ## Direct Substitution

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 $s(t) = e^{-\frac {t}{2}}cos(2t)$

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

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

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 $\frac {d^2s}{dt^2}$ 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...

2. ## Re: Direct Substitution

Hey astuart.

Basically it's asking you to calculate the derivatives and then substitution those into the equation and show that it equals zero.

So s = s(t) is your original equation while ds/dt is the first derivative and d^2s/dt^2 is the second derivative.

3. ## Re: Direct Substitution

Originally Posted by chiro
Hey astuart.

Basically it's asking you to calculate the derivatives and then substitution those into the equation and show that it equals zero.

So s = s(t) is your original equation while ds/dt is the first derivative and d^2s/dt^2 is the second derivative.
Thank you, that makes sense now