Damped Forced Harmonic Motion (part 2)

I said on the first page on Harmonic Motion that the resistance of the ocean to rapid movement tends to damp out any excessive changes in sea-level i.e. the amplitude of the tides. What is not so intuitively obvious is that the greater the damping effect the less rapid is the change from 90deg phase shift to no shift. When damping is introduced, instead of abruptly switching from one state to another the amount of shift smoothly decreases over a small range of latitudes, decreases much more rapidly across the resonance point, and then finally slows its rate of decrease again as it approaches zero i.e. instead of a "cliff-edge" effect, the graph of shift against latitude is much more S-shaped. This means that until we get far from resonance the amount of shift will not be simply zero or 90deg - it will be rather more than zero below resonance and rather less than 90deg above it. Translated into movements of the tidal bulge, a bulge directly opposite the Moon (i.e. at zero degrees) when there is no damping will sit slightly ahead of the Moon (i.e. at slightly more than zero degrees) when damping is taken into account. This is exactly what one would expect from the simple "the friction drags the bulge forward" description. However, a bulge 90deg ahead of the Moon with no damping will actually sit at less than 90deg when damping is added, not more than 90 i.e. rather surprisingly it moves slightly backwards, not further forwards.

Click here to see all these effects demonstrated using the spring model - there is now an extra link describing the effects of increased damping.


Back