# Homework Help: Air resistance Differential Equation Help

1. Mar 15, 2005

### $id Hi guys I need help solving the following differential equation for air resistance d^2s/dt^2 + R ds/dt = g Where g = gravity I presume and R = k/m where k = resistance constant Using my limited knowledge I think that the auxiliary equation for this is Y^2+ RY = 0 Y = 0 or R General Solution S = A + Be^Rt Which log graph would i need to plot to work out resistance constant. thanks a lot sid 2. Mar 15, 2005 ### dextercioby You meant "-R" and $...e^{-Rt}$ ("R" positive,i presume). Linearize the equation.U'll find R from the negative slope... Daniel. 3. Mar 15, 2005 ###$id

Is the actualy equation correct though?

Or am i missing something

sid

BTW by linearise i think you mean

ln(S)=LnA + LnB -RT

So a plot of Kn(S) against T for some values should yeild the gradinet at -R

yeah ?

4. Mar 15, 2005

### dextercioby

Yes,for the second part.The initial equation may be correct,i don't know how u've gotten it.But the solution you had found was incorrect.

Daniel.

5. Mar 15, 2005

### $id So the general solution is wrong? 6. Mar 15, 2005 ### dextercioby For the homogenous eq.is correct $$s(t)=A+Be^{-Rt}$$,with R>0... Daniel. 7. Mar 15, 2005 ###$id

well g is constant as it = to 10

so isnt the equation homogenous in essence

sid

8. Mar 15, 2005

### dextercioby

No,a homogenous is when the constant is 0.

Daniel.

9. Mar 15, 2005

### $id ok fair enough, The orginal differential equation is definate correct, it was taken from a book What do you reccomend for solving that equation sid 10. Mar 15, 2005 ### dextercioby You tried one way.Try differently.Make a substitution $$\frac{ds(t)}{dt}=:u(t)$$ Daniel. 11. Mar 15, 2005 ###$id

Unfortunately i am not aware of that method

the only ones i know are auxiliary equation, seperation of variables and intergrating factors

Do you which one of those will work.

sid

12. Mar 15, 2005

### dextercioby

Separation of variables...?Write the new equation.You'll see that the variables would be separated.

Daniel.