Quieting T-post drivers

A quick tutorial on controlling noise and vibrations.

Picture a piano string in your head. A hammer thumps it

And the string deflects. Because of the interactions between the mass and the springiness, the string vibrates.

If the hammer hits the string where it cannot move then no energy is transmitted to the string. Work = energy = force * distance. If distance = zero, then energy is zero.

An even simpler conceptualization of a vibrating system

There are different forcing functions. Systems where the force is applied through a long period of time are dominated by stiffness. The energy injected into the system is a function of (1/K)^2. Since the stiffness of a plate in bending is proportional to T^3, increasing material thickness decreases the system's ability to accept energy from the forcing function.

If the forcing function is a quick impulse (momentum deposition) then the system is mass dominated. Mass goes up in proportion to T.

Damping
Damping is energy dissipation.

Most commercial solutions involve adding damping. They work well for excitations like electric motors where the forcing functions are continuous. Without damping, the oscillations grow and the noise level is obnoxious. With damping, the oscillations never grow and the noise levels never grow to unacceptable levels.

Adding damping is less dramatic for impulse excitations. The peak level attenuates quickly but the peak level is not much lower than it would be without the damping.

BUT....
Data rules.

Let's have a horse race.

I think the winner will be increasing the thickness of the cap. Increasing the thickness of the cap both increases the stiffness and the mass where the impact occurs. I can also sneak in a little bit of damping if I put slug of steel inside the driver and sandwich a tiny bit of butyl rubber between the slug and the end-cap of the driver.

But I will give the other proposals a shot if I can fab them up.