Consider a particle moving in a path described by a concentric helical spring

 

How would you mathematically describe the displacement when the spring is expanded.

 

As the particle is displaced along x, y and z axes simultaneously.

 

Do we need partial differential equation in 3 dimensions to describe the motion?

 

Please advise.

 

Thanks in advance.

You need to formulate your question more exactly.

 

"A particle is moving.."

 

With steady velocity? Accelerating? What?

 

"If the helix is expanded"

 

How?

Radially? Axially? Is the spring subject to the radial contraction that would accompany being pulled out along an axial direction?

 

Is the particle subject to the same forces that expand the spring or how does it receive its change of direction?

 

Why is it moving, is it like a bead sliding down a vertical spring or what?

You need to formulate your question more exactly.

 

"A particle is moving.."

 

With steady velocity? Accelerating? What?

 

"If the helix is expanded"

 

How?

Radially? Axially? Is the spring subject to the radial contraction that would accompany being pulled out along an axial direction?

 

Is the particle subject to the same forces that expand the spring or how does it receive its change of direction?

 

Why is it moving, is it like a bead sliding down a vertical spring or what?

 

To elaborate.

Axially with radial contraction. A particle that moves along the path defined. (an imaginary particle).