A particle of mass ? moves in one dimension along the ?- axis. Its potential energy...

A particle of mass ? moves in one dimension along the ?- axis. Its potential energy is given by ?(?) = ??3 − ??, where ? and ? are positive constants.

(a) Calculate the force on the particle, ?(?). Find the position of all equilibrium points and identify them as stable or unstable.

(b) Draw an energy diagram showing the potential energy U, the kinetic energy K, and the total mechanical energy E for bound motion. Show the location of the stable and unstable equilibrium points on your diagram.

(c) What is the minimum kinetic energy required for the particle to be unbound?

(d) Find the period of small oscillations around the stable equilibrium.

(e) Estimate the maximum displacement from equilibrium for which the small oscillation approximation is valid to 1 percent accuracy.

Expert Solution

genius_generous answered 2 years ago

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