Concepts : Destructive waves vs. equilibrium

[Essenar]

Homework Statement

An upward and downward pulse, otherwise identical in shape are propagating in opposite directions along a stretched string. At the instant they overlap completely, the displacement of the string is exactly zero everywhere. How does this situation differ from true equilibrium?
HINT: Where is the wave energy?

Homework Equations

The Attempt at a Solution

I'm assuming that for wave 1, amplitude = +A and for wave 2, amplitude = -A.
y1(x, t) = A1 cos((k1)x - (w1)t + phi1)
y2(x, t) = -A1 cos ((k2)x + (w2)t + phi2)
No phase change so phi's drop, +/- symbols to indicate opposite directions. Now, while they cancel, I'm assuming that even if there is 0 displacement, there is still energy in both waves. However I'm having trouble proving it.
Thanks guys and I hope I posted this properly.

 

[ehild]

The spring has both kinetic and potential energy. At the instant the displacement is zero along the whole spring, PE=0 and KE is maximum.

ehild