Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What is the formula for max kinetic and max potential energy of a spring?

share|cite|improve this question
Writing "concept" in the title doesn't really change this from a "give me the formula" question. As always you would use the definition of work and because your context is springs you would use Hooke's law for a first approximation. – dmckee Nov 20 '12 at 14:26

Well, what's the equation for the kinetic and potential energies of the spring in general? Based on that, for what values of displacement will they be maximized?

share|cite|improve this answer

I think you mean the energy of a particle attached to a spring. In that case the total energy is given by $$E=K+P=\frac{1}{2}mv^{2}+\frac{1}{2}kx^{2}$$ Where $m$ is the mass of the particle, $v$ is the velocity of the particle, and $x$ is the distance of the particle from the origin. So, the maximum of potential energy $P$ is given when the kinetic energy $K$ is zero (i.e. when $v=0$, in the turning points of the particle). In that case $E=P_{max}$. So $$E=P_{max}=\frac{1}{2}kx_{max}^{2}$$ here $x_{max}$ is the maximum stretch of the spring (i.e. the turning point, $v=0$).

In the other hand, the maximum of kinetic energy is given when $P=0$ (it occurs when $x=0$), i.e. $E=K_{max}$, or $$E=K_{max}=\frac{1}{2}mv_{max}^{2}$$ where $v_{max}$ is the maximun velocity of the particle, it occurs when the particle passes through the origin (i.e. when $x=0$).

share|cite|improve this answer
Seems good but a better term for $x$ would be the displacement from the origin. – Calc1DropOut Apr 16 '14 at 8:09
That's exactly the meaning of my $x$. – Ana Apr 17 '14 at 17:56

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.