I was asked to determine the shear forces on 12" diameter table legs supporting a few hundred pounds of static weight.
How does one calculate or determine the potential force on the legs and/or potential collapse of the legs given an earthquake? The legs are not secured to the flow.
Where can I find information that will help me answer the question of potential collapse during an earthquake?
Your question is a very broad one. Assuming your needs go beyond simply the analysis of a driven simple harmonic oscillator, you should search for information in the area of "earthquake engineering."
You might find suitable online references, or the names of appropriate textbooks, here:
The Earthquake Engineering Online Archive NISEE e-Library
Your comment indicates your question is really a practical one about safety in the laboratory. You are right to be concerned, I've been in labs during moderate earthquakes and seen that people's safety, not just expensive equipment, is at risk. You should contact your university's/company's safety officer about steps to reduce seismic hazards in your lab. Usually this means strapping heavy equipment to a wall to prevent it from tipping over. You could check with the manufacturer of the table to determine what its rated load capacity is. Check out information at USGS and FEMA regarding earthquake preparedness at home and work.