Is My Solution for Centripetal Force in a Spiral Orbit Correct?

[cemtu]

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?

 

[PeroK]

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]

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]

The formula has been corrected in the original post. Thank you!

It looks correct to me.