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**Unoticed** In terms of cylindrical polar coordinates the whirlpool-like surface

z*p^1/2 = −1, z < 0 is formed by rotating a branch of a function z = −1/x^1/2 about a vertical asymptote (the z-axis). A particle of mass m slides on this smooth surface and experiences the action of the gravitational force.

Part 1 of the question was to show that the Kinetic energy, T + the potential energy, V was equal to E (i.e. that energy is conserved). This was done ok.

Can anyone try to explain what the following part of the question means?

For what value of z0 the motion at constant height z0 is possible, i.e. z(t) = z0 for any t?