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It is well known that shaking babies can cause serious brain damage, but what exactly constitutes shaking? I've seen some videos that demonstrate shaking on dolls, and I can say with certainty that I don't do that. But at the same time, the motion of a rocking chair is not nearly enough to soothe my 2 month old when she's worked up, and larger amplitude or higher frequency movements are useful to calm (or at least quiet) her.

Some motions that are effective include something like a bicep curl, various types of bouncing, and going over a rough gravel trail that jostles her stroller a lot. In all these cases, her head and neck are supported, which is a big difference from the shaking I've seen in videos. At the same time, the accelerations are not trivial. If someone subjected me to the same accelerations, I'd find some of them unpleasant. Even with the head and neck supported, there must be some level of acceleration that is harmful.

We also have a snoo, and some of its motions seem pretty aggressive. One setting can cause her head to wag side-to-side by a fair amount.

The fact that these motions are calming may suggest that they're safe. However, I worry that it's like brain injuries in football: concussions get all the headlines, but the cumulative effect of a lot of small impacts is just as dangerous.

Danger often exists on a continuum, but experts often come up with some safety threshold to stay below. Where is that threshold for baby motion? What exactly constitutes shaking?

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Shaken baby syndrome is, when oversimplified, a severe concussion with significantly increased effects on a baby.
Just to be clear, there are more concerns than the brain injury, but your question seems to focus on the brain injury as you're asking about cases where the baby's head is supported.

Babies are more at risk than adults because their brains are still developing and thus more vulnerable, and also because their lack of neck strength to hold their head up leads to more severe head swinging when being shaken, increasing the trauma to the brain comparing to shaking an adult.

For obvious reasons, there is no precisely measurable limit of what is shaking and what (barely) isn't, but you're looking at the ballpark of concussion levels of head trauma.

Some motions that are effective include something like a bicep curl, various types of bouncing, and going over a rough gravel trail that jostles her stroller a lot.

None of these are in the concussion ballpark. Relative to a baby's size, these are the equivalents of driving over cobblestone or riding a horse.

As long as your baby's head isn't violently shaking about, which this doesn't particularly sound like, then it's nowhere near the kind of violence you need for shaken baby syndrome.

If someone subjected me to the same accelerations, I'd find some of them unpleasant.

Unpleasant, yes, but you wouldn't be concussed because of them. These accelerations are still not even in the ballpark of extreme sports or e.g. rollercoasters, and these (barring accidents or falls) don't automatically cause concussions either.

Even with the head and neck supported, there must be some level of acceleration that is harmful.

Yes, but that requires a non-trivial amount of acceleration that you're not going to easily find on human strength alone. At the very very least, you'd have to be making an active and concerted effort to jostle the baby's head/brain.

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What you are talking about is shaken baby syndrome.

Babies have weak neck muscles and often struggle to support their heavy heads. If a baby is forcefully shaken, his or her fragile brain moves back and forth inside the skull. This causes bruising, swelling and bleeding.

Rocking a child in rocking chair for example is not going to be vigorous enough to cause that kind of damage.

Imagine a ball inside a box filled with water. Maybe you can make something like this up with a sealed perspex box. The ball is to represent the baby's brain, and the box is the skull. This is how it is inside anyone's head.

American Footballers, and other sports people in contact sports are always having to be checked for concussion after a nasty tackles and this is for the same reason. Their brain hits the inside of the skull causing bruising (see the true story movie, Concussion).

If you move it rhythmically and slowly, the ball may touch the sides lightly, but not cause any damage. Shake it though and the ball will bang on the sides of the box. Being the brain, it has the potential to suffer serious trauma and damage. This damage can even lead to death.

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