OK I have a slightly new problem that seems much more difficult.
= kinetic friction coefficient
= cross sectional area
I am trying to solve and then solve the specific function as an initial value problem.
I just need help solving for now. I should be OK after that.
This is for a hobby physics project, not for homework.
I am still confused. If I differentiate both sides I will get right? which is what I started with. This equation is my work thus far on taking the antiderivative of .
If I substitute then I get The antiderivative of this part isn't as simple as is it? Even so I would end up with and I don't know .
I forgot two negative signs, not that it matters much here but it should be:
I previously solved the initial value problem for constant acceleration as a differential equation:
which is our familiar physics equation
You can the solve the specific function and find B,C,D given 3 X(t) samples.
Now, instead of assuming a constant acceleration, I am trying to solve this with and that is how I got
It is not obvious to me yet how many X(t) samples I will need to solve this as an initial value problem?
I worked through it with my differential equations prof and got to:
I verified the previous equation against simulations as well as with mathematica. Next I used matlab and then simplified to get back to :
With the two unknowns,
I was expecting it to have a single not ?
This will be messy to solve as an initial value problem but possible.
Is there any way to make this function continuous? Tan() and Sec() make these hard to use and I don't see why it is necessary.