# Deterministic non-harmonic motion of a single spring

Is there anything describing a spring's motion when e.g pulled and released, or pushed and released, with no mass-body attached to the spring. I.e not your usual "mass motion on a spring"-equation.

I'm looking for a description of a spring in motion that doesn't deal with any external inertia or force. Intuitively the motion is non-harmonic and the spring just quickly contract or extract back to ground state and briefly vibrate frenetically. Does is exist a deterministic description of this motion?

• Do you mean a damped harmonic oscillator? – Qmechanic Nov 15 '17 at 23:00
• @Qmechanic That's more or less my question. Can this be viewed as a damped harmonic oscillation, as in when dealing with predictive counter forces (e.g friction). – niCk cAMel Nov 15 '17 at 23:06
• $\uparrow$ Yes. – Qmechanic Nov 16 '17 at 5:37
• Then the tricky part is to compute m since there's no external body, m is the mass of the spring itself, but distributed along the spring, and k is not constant everywhere along the spring – niCk cAMel Nov 16 '17 at 19:56
• Check out library.wolfram.com/infocenter/MathSource/7773 if you are into Mathematica notebooks. The problem basically the same as longitudinal vibrations of a rigid rod where the only mass in the system is the rod itself. – Bill Watts Jan 11 '19 at 1:59