Demonstration of Forced Harmonic Motion

In this demonstration the lunar tidal surge is represented by the movement of the attachment point of the spring - this is called the "exciter" in the diagram. The oceanic tides are represented by the spring itself - this is called the "resonator" in the diagram. The natural frequency of the freely-propagating standing-wave is determined by the spring constant and the weight of the mass. The dissipation caused by the interaction between the oceans and the surface of the Earth is represented by the "attenuation". The magnitude of these numbers is not relevant - I have simply chosen values which illustrate the various modes well.

The information of interest is given in the middle of the diagram - values for the tidal surge are in red, for the actual tides in blue. The driving frequency and tidal frequency (shown by the Greek letter omega) are both given in a rather strange unit (radians per second) but for our purposes the number can be taken to represent the number of tidal bulges passing a given point per day: the value for the tidal surge is thus 2. The extent of the motion of each tide (shown by the letter A) shows how big the actual tide is compared to the tidal surge (the value of which is set at 2 by the model itself). The lag between the tidal surge and the actual tides (black text, Greek letter phi) is also given in a "mathematical" form - in units of Pi, in fact. For our purposes however, a value of 0 means "Full Moon equals High Tide" and a value of 1 means "Full Moon equals Low Tide".

Three different ways of showing the results graphically are available: the most interesting are the top and bottom ones. Clicking on the radio button next to "Elongation" shows the motion of exciter and resonator; "Phase difference" shows how sudden the switch from no phase shift to 90deg phase shift is in the modelled situation.

To change a number, click in the appropriate box, delete the existing value, and type in a new one.

Hope that's clear! If not, just remember that the top number of each red or blue pair shows the number of tides per day, the second number of the pair shows how high the tide is, and the black number shows whether the Full Moon aligns with high tide (a value of about 0) or low tide (a value of about 1).