An object of mass m=1 is thrown in a uniform gravitational field g with some initial speed v at some angle theta. It is shaped however such that it experiences a frictional force proportional to its velocity: Ffriction = -kV,where k is simply a constant of proportionality.
Write down and solve the two differential equations describing the motion of the particle r(t) = x(t)X + y(t)Y. You may find the ansatz for the particular integral rPI(t)= (At)Y useful.
I have been trying to do this question and I have got an answer from this but I am unsure if it is correct because of the suggestion that (At)Y is the particular integral as I didn't get this. I am in desperate need for this question to be answered as there as a lot of follow up questions after this. I understand the forces acting on this particle, however I am expecting to get a second order ODE for my y direction but I am only getting a second order for my x direction which wouldn't make sense.
If anyone can help I will be very grateful!
Thank you!
Write down and solve the two differential equations describing the motion of the particle r(t) = x(t)X + y(t)Y. You may find the ansatz for the particular integral rPI(t)= (At)Y useful.
I have been trying to do this question and I have got an answer from this but I am unsure if it is correct because of the suggestion that (At)Y is the particular integral as I didn't get this. I am in desperate need for this question to be answered as there as a lot of follow up questions after this. I understand the forces acting on this particle, however I am expecting to get a second order ODE for my y direction but I am only getting a second order for my x direction which wouldn't make sense.
If anyone can help I will be very grateful!
Thank you!
