Periodic Force Action: Can It Displace a Particle Without Integration?

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Discussion Overview

The discussion centers on the effects of a periodic force, specifically F(t) = F0sin(ωt), on a particle initially at rest. Participants explore whether this force can displace the particle significantly over time without integrating the Newton equation, examining the implications of the force's nature and initial conditions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the sine function allows for continuous positive displacement of the particle, as momentum gained during the positive lobe is lost during the negative lobe, maintaining a non-negative velocity.
  • Others argue that a cosine function would not achieve the same displacement, suggesting that it leads to oscillation around the initial position rather than drift.
  • A participant questions the interpretation of the force as a scalar and its implications for directionality, indicating a potential misunderstanding of the problem's setup.
  • It is noted that the initial phase of the force is crucial, with the sine function leading to drift while the cosine function results in oscillation.

Areas of Agreement / Disagreement

Participants express differing views on the effects of the sine versus cosine functions on particle displacement, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Participants discuss the implications of initial conditions and the nature of the force, but there are unresolved assumptions regarding the interpretation of the force's directionality and its representation as a scalar.

Bob_for_short
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It is not a home work.

Let us suppose that at t=0 a particle is at rest. At t=0 we switch on a periodic force F(t) = F0sin(ωt). Without integrating the Newton equation, do you think such a force is capable of displacing the particle to very far places as the time goes on?
 
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Yes. I think a cosine would not.
 
DaleSpam said:
Yes. I think a cosine would not.

Right answer, congratulations!
.
.
 
What is the thinking behind this solution? Was it reached mathematically (but without integrating the Newton equation) or intuitively?
 
Kind of a little of both. During the positive lobe of the sine wave the object gains momentum. Then during the negative lobe it loses momentum. The amount of momentum gained is equal to the amount lost (effectively an integration in my head) so the velocity is always positive or zero, never negative.
 
Bob_for_short said:
It is not a home work.

Let us suppose that at t=0 a particle is at rest. At t=0 we switch on a periodic force F(t) = F0sin(ωt). Without integrating the Newton equation, do you think such a force is capable of displacing the particle to very far places as the time goes on?

Although I infer (perhaps wrongly) that you mean to say the force would be rotating and thus changing direction periodically, it seems from looking at your equation that the force will merely be scaled with time, and not redirected. Even though there is an angular velocity in the sin function, the sin function still results in a scalar. Could you specify which assumptions I wrongly made or more likely, should have made?

edit: Upon thinking it over, I think you do mean it as a scalar and a one dimensional problem. In that case I suppose it does matter if the problem starts with maximum force (cosine) or with minimum force (sine)...
 
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Exactly! It is a 1D problem. It happens that the initial phase of the force is important. Only in the particular case of cos(ωt) the particle oscillates around the initial position. In any other case the particle "drifts" away.
 
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