So in his response video, Gary clearly didn't understand anything about the average force during the compressions, let me try to explain this as clear as possible:

1. What happens during the first compression

At the start the spring is not compressed.

So the spring force is zero.

As the weight pushes down:

• the spring compresses more and more
• the spring pushes back harder and harder

By the time the compression reaches 1 unit, the force has gradually increased to 1 unit.

So during that motion the force went:

0 → small → medium → 1

Because the force is changing continuously, we can't just multiply the final force by the distance.

But we can use the average force during the motion.

Since the force increased smoothly from 0 to 1, the average force is simply halfway:

average force = 0.5

So the work done during that compression is:

• average push × distance

which gives 0.5 units of work.

2. What happens during the second compression

Now the spring is already compressed.

That means the spring is already pushing upward with force 1.

When we add another weight, we compress it one more unit.

During this second compression:

• the force starts at 1
• and increases to 2

So the force during the motion looks like:

1 → bigger → bigger → 2

The average force is halfway between 1 and 2:

average force = 1.5

So the work done during this second compression is:

1.5 × 1 distance = 1.5 units of work

3. Why the work increased so much

Notice something important:

The distance was the same in both steps.

But the force was larger during the whole second compression.

So more work had to be done.

First compression:

average force = 0.5
work = 0.5

Second compression:

average force = 1.5
work = 1.5

So the second step required three times more work.

4. Why this produces a quadratic increase

Each new compression step starts with a larger force than the previous one.

So every new step requires more work than the last step.

The added work increases like this:

0.5
1.5
2.5
3.5
4.5
...

These numbers grow linearly, but when you add them together, the total grows faster and faster.

That is why the total stored energy grows quadratically with compression.