Classical Mechanics: Finding the centripetal force acting on an object that moves within a spiral orbit.

Homework Statement:

In polar coordinates find the force as a function of radial coordinate F(r) that allows a particle to move in logarithmic spiral orbit r=k*e^(α*θ) , where k and a are constants.

Relevant Equations:

## \frac{d^2}{dθ^2}(1/r)+1/r=(-μr^2)⋅F(r)/l^2 ##
I believe I solved this. Is this solution true? Can please anyone just check?

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Answers and Replies

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PeroK
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Homework Statement:: In polar coordinates find the force as a function of radial coordinate F(r) that allows a particle to move in logarithmic spiral orbit r=k*e^(α*θ) , where k and a are constants.
Homework Equations:: ## \frac{d^2f}{dx^2}(1/r)+1/r=(-μr^2)⋅F(r)/l^2 ##

I believe I solved this. Is this solution true? Can please anyone just check?
The force must depend on the speed the particle is moving.

cemtu
The force must depend on the speed the particle is moving.
what do you mean, sir? The formula(homework equation) is given like as I wrote up there.

PeroK
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what do you mean, sir? The formula(homework equation) is given like as I wrote up there.
What is the force on an object moving in a circle? It depends on ##\dot \theta##.

cemtu
What is the force on an object moving in a circle? It depends on ##\dot \theta##.
The formula has been corrected in the original post. Thank you!

PeroK
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The formula has been corrected in the original post. Thank you!
It looks correct to me.