Quick question about equilibrium points

[auk411]

Homework Statement

In simple harmonic motion (especially with a spring), does the kinetic energy equal the potential energy at the equilibrium point? In other words, does K = U?

If not, is there a time when the kinetic energy does equal potential energy in simple harmonic motion.

Homework Equations

Total energy = K + U = 1/2 KA^2, where A is the amplitude of the displacement function.

The Attempt at a Solution

 

[Mindscrape]

Sure, K=0, and there is no displacement so there is no potential energy.

You could also do the other bit you propose, but you would need to assign some initial conditions such as initial position and initial velocity.

 

[auk411]

Sure, K=0, and there is no displacement so there is no potential energy.

You could also do the other bit you propose, but you would need to assign some initial conditions such as initial position and initial velocity.

I'm not sure what parts you are referring to. Also, I'm thinking about a general solution. Your first comment just seems to apply when, essentially, nothing has happened. For example, before I pull a block back attached to a spring and it is just sitting there at the spring's natural length, then k =0. After pulling it back to distance D, and letting it go, it then will cross over the equilibrium point again. But the velocity will not be 0, and hence k cannot be 0.

At the bottom of this, I get the basic concept, what is really tripping me up are knowing what signs to attach to K and U. (E.g., why doesn't k = - U at Equilibrium point?)