Hi, the two forces acting on an object are its weight and air resistance. In my differential equations coursework I begin with 'air resistance = -kv' where v is the velocity and k is a constant. This is easy enough to solve.
Findgin auxiliary equation
Finding particular integral
General Solution
when
Therefore
when
So the equation is
I would appreciate if you could first check the correctness of the above working.
My main question is: how do you find the differential equation when the air resistance = -kv^2
This time the air resistance is dependent on the square of the speed rather than the speed. Newton's second law becomes:
I am looking to solve this for s as I did for the other equations.
Thanks, I didn't realize I was overcomplicating it, although I'm still not sure about how to solve the second equation. It should be exactly the same except with a different auxiliary equation (or general equation, as running-gag called it). I'm not sure what the auxiliary equation is for the second case, any of you know?