Light springs with the same spring constant are attached to light
particles and joined to the corners of the following rigid frames,
drawn on unit grids (assume that the pentagon and the
small triangle are regular):
In each case, where will the particle be at equilibrium and how
long will the springs be?
Can you devise any frames for which the equilibrium point would lie
outside the frame? On the frame? Can you devise any frames with
multiple equilibrium points?
Imagine pulling the particle slightly in each case. In which
directions will the particles oscillate to and fro in a straight
line? For what sorts of frames would this always be possible?
If one of the
springs has double the spring constant of the other springs in each
case, where would the equilibrium points lie?