What is the surface height of a still pond after an object is dropped in it?

[Michael12345]

I had an idea for a project that would make use of a formula for the surface height of a body of water after an object was dropped in it. I wouldn't need a time-dependent equation, just a nice snapshot...although a general equation (a function of x, y, and t) would be nice. I haven't had much luck finding a solution online, but I'll keep looking. I'm comfortable with undergrad level math and physics, so I don't mind doing some heavy lifting. And if you don't have the time, but can point me to a resource or two, I'd appreciate that, as well.

Thanks,
Michael

 

[Andy Resnick]

Here you go:

http://farside.ph.utexas.edu/teaching/315/Waves/node50.html

 

[Bill_K]

An excellent and very thorough book on the subject is "Water Waves" by J J Stoker. And by good luck the full text is available online at www.archive.org. Sect 6.6 is "Discussion of the motion of the free surface due to disturbances initiated when the water is at rest." On or about p 170. Included are formulas, graphs and some photos, although the photos don't show up very well online.