A spring in a smooth table
A particle of mass m moves without friction in a horizontal table
while tied to a fixed point through an elastic spring of constant k
and length l. The equations of motion are as follows (each prime is
a time derivative):
m x''+k [1-l (x2+y2)-1/2]
x=0
m y''+k [1-l (x2+y2)-1/2]
y=0
On the right the mass orbit is displayed, along with the
return circles (i.e., the maximum and minimum distances in the orbit).