In simple harmonic motion (SHM), there are two important ideas to know: maximum displacement and average velocity. Let’s break them down into simpler terms.

Maximum Displacement
Maximum displacement, also called amplitude, is how far an object moves from its resting position during its movement.

Imagine a mass hanging on a spring. When you pull the spring and stretch it as far as it can go before letting it go, the maximum displacement is the furthest distance the mass travels from its normal spot.

If we call the maximum displacement "A", then we can say at the highest point the mass reaches, the displacement is $x = A$.

Average Velocity
Now, average velocity in SHM is a little more complex. Average velocity is found by taking the total displacement (how far the object has moved) and dividing it by the total time it took.

In a full cycle of SHM, the object goes back to where it started. This means that the total movement or net displacement is zero. So, if you find the average velocity for one complete cycle, it looks like this:

$$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{0}{T} = 0$$

Here, $T$ represents the time it takes for one complete cycle. This shows us that even though the mass is moving back and forth quickly, the average velocity over one entire cycle is zero because it ends up where it started.

Conclusion
To sum it up, maximum displacement tells us about a specific highest point in the motion, while average velocity looks at the overall trip over time. This means that during periodic motion, the average velocity can be zero, even though the object is moving a lot.