- #1
mma
- 245
- 1
speed?
This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky.
In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite speed, in the sense that any after any [itex]\varepsilon>0[/itex] time after releasing the upper end of the hanging slinky, the displacement of the lower end of the slinky is greater than 0.
In contrast, in the continuous limit, there is a [itex]\varepsilon > 0[/itex] time interval so, that after releasing the upper end of the hanging slinky, the lower end remains exactly motionless during this interval.
However, this is only a special case, assuming a special (linear) force law between the masspoints, I conjecture that for a broader class of force laws (or any force law) this feature holds. Is it true, or I'm wrong, and this effect is due to just the linear force law?
This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky.
In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite speed, in the sense that any after any [itex]\varepsilon>0[/itex] time after releasing the upper end of the hanging slinky, the displacement of the lower end of the slinky is greater than 0.
In contrast, in the continuous limit, there is a [itex]\varepsilon > 0[/itex] time interval so, that after releasing the upper end of the hanging slinky, the lower end remains exactly motionless during this interval.
However, this is only a special case, assuming a special (linear) force law between the masspoints, I conjecture that for a broader class of force laws (or any force law) this feature holds. Is it true, or I'm wrong, and this effect is due to just the linear force law?