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Graduate Advising


K-State Online


K-State Physics







Michael J. O’Shea


Advanced Mechanics Problems



Some more advanced but interesting mechanics problems

Crossing a river with variable current.  The optimum (minimum time) path across a river where the speed of downstream current varies in some complex way.  This is an interesting problem that can be solved analytically via non-linear differentials equations for a wide range of current profiles.  The problem can also be mapped onto the well-known mathematical pursuit problem for simpler cases




Elasticity and mechanical advantage.  Mechanical advantage can be obtained by pulling sideways on a fixed rope.  This problem turns out to be mathematically complex but can be solved exactly for the case where the pull is at the mid-point of the rope.  For other cases, numerical solution is required. 




An oscillator with harmonic and anharmonic cross-overs. Related to the previous topic, a mass at the center of a rope will undergo oscillations if dropped.  This system shows interesting cross-overs between two different types of harmonic oscillator along with a non-linear regime as a function of amplitude.  In one respect this work is the dynamic analog of the previous case.  Here the mass is dropped, in the previous case the mass (or force) is applied and the static properties are examined.