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A body attached to a spring experiences fluid friction such that its motion is overdamped. It is displaced from equilibrium and then projected with an initial velocity directed toward the equilibrium position. Which statement is correct?
- It can cross the equilibrium position only once, and only if the initial velocity is sufficiently large
- It can never cross the equilibrium position
- If the initial velocity is large enough, it can oscillate about equilibrium a few times before stopping there
- If the initial velocity is large enough, it can oscillate about equilibrium a maximum of two times before stopping there
Correct answer: It can cross the equilibrium position only once, and only if the initial velocity is sufficiently large
Solution
Overdamped systems do not oscillate. If released from rest it just creeps back to equilibrium without crossing. If given an inward initial velocity that is large enough, it can overshoot and cross the equilibrium once, but after that the strong damping prevents any further crossing. So at most one crossing is possible, only if the initial velocity is large enough.
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