Welp, heres the last of my problems. As you can tell im quite the calc dunce. So we are basing this on Newton’s second law to derive the force balance (E).
m(dv/dt) = -ks, Newton’s 2nd law, where v = ds/dt.
So what they are asking to do is replace –ks with –f(s), a continuous, odd function. This looks like
m(dv/dt) = -f(s)
from there we multiply both sides by ds/dt.
Heres what right side looks like:
-f(s) (ds/dt) = -d/dt [ (INT s(0) to s) f(τ) dτ]
(note: t and τ are not the same var.)
I have no idea how to diff/ integrate this. “INT s(0) to s”
just means the integral from s(0), bottom, to s, the top.
I guessed maybe the answer is just f(t) but im thinking not. Sorry for the big jumble, its hard type all these complex functions.
Let me know if this doesn’t make sense. Thank you!