Classical Mechanics (Kibble & Berkshire) · Problem 4.16

Linear oscillations — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · resisted-motion-linear-quadratic-resistance

Problem

A body of mass mm is projected with speed uu in a medium that exerts a resistance force of magnitude (i) mk∣v∣mk|\boldsymbol{v}|, or (ii) mK∣v∣2mK|\boldsymbol{v}|^2, where kk and KK are positive constants and v\boldsymbol{v} is the velocity of the body. Gravity can be ignored. Determine the subsequent motion in each case. Verify that the motion is bounded in case (i), but not in case (ii).

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