Mass-Spring Equilibrium Point: Affect on Position, Velocity, & Acceleration

[The Head]

Somehow I have become confused about the different parameters of a damped mass-spring system that follows:

my'' + cy' + ky = 0

When the mass-spring system is oscillating, but passing through its equilibrium position (y=0), the third term will be zero. And from the best I can rationalize, the acceleration is also zero at this point and the velocity is maximal. Thus the first term is zero and the second non-zero. So I am left with one non-zero term equal to zero.

Where is the flaw in my reasoning? Thanks.

 

[Doc Al]

When the mass-spring system is oscillating, but passing through its equilibrium position (y=0), the third term will be zero.

So far, so good.

And from the best I can rationalize, the acceleration is also zero at this point and the velocity is maximal. Thus the first term is zero and the second non-zero. So I am left with one non-zero term equal to zero.

The acceleration y'' will only be zero if both other terms are zero (or add to zero). As long as it's moving, there will be a damping force (second term) and thus an acceleration at y = 0.