Coil Movement

Do you mean that you want your object to move along a path that is shaped like a coil ( say a spiral staircase )

t = time;
x = a cos t;
y = b sin t;
z = fun(t); // most likely some linear function of t
// like z = 0.2 t;


or do you mean like an object hanging from a coil spring, bouncing up and down?
easiest: assume coil is just a spring with no x, or y motion.
no damping, and no induced rotation.
t = time;
x = x;
y = y;
z = A sin( wt + C );
A = amplitude;
w = frequencey ( kinda )
C = related to initial displacement

if it is the second case, and you want something more complicated, just give a better description of what kind of motion you are trying to simulate.