[Ian]

Here is what my engineering colleagues had to say about the question before us. I have translated from engineering-speak as well as I could.

The problem of a weight (mass) moving along a rod that in turn strikes another object is really quite complicated and we do not have enough information to answer your question. Here is a somewhat lay interpretation of the problem, which we have modified from The Physics of Baseball by Robert K. Adair.

Basically, the properties of a rod (sword, bat) relevant to striking another object squarely are defined by three weight distributions, or three moments.

1. The sum of the weight of each part of the sword, which is just its total mass (the zero moment)

2. The sum of the weight times distance, measured from the handle, of each piece of the sword (the first moment)

3. The sum of the weight times the square of the distance for each piece of the sword (the second moment or the moment of inertia)

There are three key positions along the sword that follow from these three moments.

a. The center of gravity
b. The center of inertia
c. The center of percussion

There are three additional factors that need to be considered.

d. The elasticity of the sword
e. The resonant frequency of the blade
f. The position of the vibrational node

Although the center of percussion and the vibrational node will be close to each other, they are not the same.

For a sword of fixed mass distribution, we can determine fairly simply the various points that correspond to the three moments.

The center of gravity is just the balance point. The center of percussion can be found by holding the sword lightly by the end of the hilt and striking the blade gently with a hammer; when the blade is struck at the center of percussion there is no detectable movement at the hilt. In most cases the center of percussion is very close to the vibrational node -- when the blade is struck at the vibrational node no vibrations are felt at the hilt.

The center of inertia can be determined by placing the sword on a frictionless surface (such as an ice rink) and pushed away. When the push is placed at the center of inertia the sword will move away without any appreciable rotation.

Each of the moments are manifest in obvious ways. The weight is felt by holding the sword vertically. The force required to hold the sword straight out in front of you at arm's length is proportional to the first moment. The force required to wave it back and forth vigorously when it is vertical is proprtional to the second moment. This second moment contributes most to the "feel" of the sword and is the factor most important to the user.

The elasticity is determined by the blade's resilience near the point of impact; a resilient blade may store energy upon impact and return that energy to the target.

The resonant frequency is a measure of the energy loss when a target is struck at a point along the blade away from the vibrational node. A higher frequency indicates a larger (i.e., longer) "sweet spot." Swords with longer blades and thicker handles will display higher vibrational frequencies and long sweet spots.

This is what we know about items that have a fixed mass distribution. When you add a varying mass distribution, the problem becomes more complex. When the weight distribution shifts, all of the moments change.

A sliding mass would create a tip-heavy sword, moving the centers of gravity, inertia and percussion away from the hilt. Depending on the fraction of the total mass that is moving and its final resting place along the blade, the respective moments may well be centered quite close to the tip, and essentially one would have a club. Such a shift in mass would likely make a clumsy and slow weapon.

We will think some more about this problem but it seems that any substantial shift in mass would produce a sword that could be difficult to control and would probably slow its action. How much of an effect would depend on the fraction of total mass that was shifting and the distance it traveled away from the hilt.