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Reg_S

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- Homework Statement
- A point particle of mass m slides without friction on inside the surface of a truncated cone. The cone is fixed , with half angle α, a bottom radius a, and a top radius b. You are to assume that the particle always remains in contact with the cone. Use ρ as a coordinate describing a location along the cone surface and θ to describe the azimuthal angle locating the particle.

- Relevant Equations
- a) Consider first circular orbits ( Constant ρ) contained within the truncated cone. What range of total energy is available?

b) Find the frequency of small oscillations about a particular contained circular orbit assumed to be ρ=ρ0 ? Express in terms of a, b, α and ω0.

c) Now consider a non-circular orbit (ρ is not constant) . Assume a particle is released the top rim with an initial velocity with components ρ(0)=0 and θ(0)= ω' >0. For what range of ω' is the motion entirely contained within the truncated cone.

I tried using coordinates system from cone, but not got what actually want to get. Any idea from you will greatly appreciated. Thanks