- #1
thetasaurus
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Not sure if this topic belongs here, but here goes.
From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable,
F(x)=-\frac{a}{b}+\frac{ba}{x^{2}}
Where a and b are constants. Now I need to get x(t)
Dividing by mass and multiplying by x^2:
x^2\frac{d^2x}{dt^2}=-\frac{ax^2}{mb}+\frac{ba}{m}
Unfortunately I do not have the skills to solve this differential equation.
x=y, \frac{-a}{mb}=b, \frac{ba}{m}=k, y'=u
y^2y''=by^2+k
I tried to eliminate the y'':
y'dt=udt
\int{y'dt}=\int{udt}
y=ut+CAnd that doesn't really get me anywhere. Anyone with knowledge of nonlinear ODEs care to help? I tried Wolfram, but even with my Pro free trial it took to much computing time and never gave me a solution.
Also since this wasn't required of the problem per se, and I just want to solve this, I'm not sure what forum it should be in.
Thanks.
Homework Statement
From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable,
F(x)=-\frac{a}{b}+\frac{ba}{x^{2}}
Where a and b are constants. Now I need to get x(t)
Homework Equations
Dividing by mass and multiplying by x^2:
x^2\frac{d^2x}{dt^2}=-\frac{ax^2}{mb}+\frac{ba}{m}
Unfortunately I do not have the skills to solve this differential equation.
The Attempt at a Solution
x=y, \frac{-a}{mb}=b, \frac{ba}{m}=k, y'=u
y^2y''=by^2+k
I tried to eliminate the y'':
y'dt=udt
\int{y'dt}=\int{udt}
y=ut+CAnd that doesn't really get me anywhere. Anyone with knowledge of nonlinear ODEs care to help? I tried Wolfram, but even with my Pro free trial it took to much computing time and never gave me a solution.
Also since this wasn't required of the problem per se, and I just want to solve this, I'm not sure what forum it should be in.
Thanks.
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