Given ℓ find the form of the potential U(r) such that the trajectory of a particle that is held to this potential is giv

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Given ℓ find the form of the potential U(r) such that the trajectory of a particle that is held to this potential is giv

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Given ℓ find the form of the potential U(r) such that the trajectory of a particle that is held to this potential is given by the spiral r(ϕ)= r_{0}e^(alpha*ϕ), where r_{0} and alpha are constants. Discuss and explain the physical system and step by step.
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