- #1
iibewegung
- 16
- 0
Hi,
(All oscillations I'll be talking about here are longitudinal.)
For coupled oscillations of 2 masses between 3 identical springs (ends held fixed by walls), I think it was a standard textbook mechanics problem to show that the lowest-frequency mode is the symmetric one (where the masses move in the same direction).
|-----o-----o-----|
1. Is there a higher-level reason for this?
(by "higher-level" I mean knowing the answer without doing the calculation ie. the "physics" answer; by "lower-level" I mean actually going through the tedious coupled ODE-solving to find out)
2. Will this be true for N masses between N+1 springs (again, ends fixed)?
I'm asking this because in the N=2 case, both masses have at least one spring to interact with. But for the "symmetric" mode (all masses moving together) in a larger-N system, the masses close to the middle barely seem to interact with any spring at all. In this case, it seems natural to imagine that the 2 masses at the ends of the chain bear all the stress of driving the motion...Any insights much appreciated!
(All oscillations I'll be talking about here are longitudinal.)
For coupled oscillations of 2 masses between 3 identical springs (ends held fixed by walls), I think it was a standard textbook mechanics problem to show that the lowest-frequency mode is the symmetric one (where the masses move in the same direction).
|-----o-----o-----|
1. Is there a higher-level reason for this?
(by "higher-level" I mean knowing the answer without doing the calculation ie. the "physics" answer; by "lower-level" I mean actually going through the tedious coupled ODE-solving to find out)
2. Will this be true for N masses between N+1 springs (again, ends fixed)?
I'm asking this because in the N=2 case, both masses have at least one spring to interact with. But for the "symmetric" mode (all masses moving together) in a larger-N system, the masses close to the middle barely seem to interact with any spring at all. In this case, it seems natural to imagine that the 2 masses at the ends of the chain bear all the stress of driving the motion...Any insights much appreciated!
Last edited: