In the following Phase Shift Oscillator ¿What is the purpose of the 2.5[V] at the non-inverting terminal?

I already developed the equations for almost the same circuit except that the non-inverting terminal is tied to ground.

I've found that the gain A = 29 so that the circuit oscillates at a frequency of f= 1 / sqrt(6)*R*C

The simulations are not consistent, as for the current circuit the sine wave seems at the output to be shifted 2.5[V] but when I put 1[V] for example the signal fades over time.
Do the 2.5[V] affect the gain or frequency? If so how?
OR
Are those 2.5[V] just for to shift the signal? Thank you.

 

What was the power supply arrangement for the circuit with the non-inverting input grounded?

 

The TLV2471 is a Rail-To-Rail Input/Output OpAmp, so when the power is +5V, then using 2.5V can be the virtual ground for the sine wave.

The original circuit at here.

 

For a sine-wave, the output needs to swing evenly plus and minus around the bias point of the op amp. If the op amp is powered from a single supply and ground then the op amp output has to be biased a 1/2 the supply voltage to avoid clipping the bottom half of the sinewave. This is accomplished by biasing the plus (+) input at 1/2 the supply voltage.

 

When I wrote this app note I had a dog named Bubba who constantly chased his tail; hence, the Bubba oscillator. The 2.5 volts is for biasing as previously mentioned.