A way to soften this is to buy a piece of spring steel at lows or Home Depot and another piece of all thread. Bolt the steel to the base, and attach the all thread to the other end. This will not only dampen the vibration but allow you a wider variety of angles to shoot from...
Granted, what works is good.
But spring steel does not dampen vibration nor harmonic oscillation. If anything, it would be the opposite, it's rather good at it. What you have is a length of metal for a mount that is not sympathetic to the vibrations and harmonic oscillations that are found at the point it is mounted
on the bike. So it's all good. If it had vibrated, you could have shortened or lengthened it to try to stop it, or added a weight or brace between the two to try to dampen oscillation.
Rubber and/or cork washers or barriers all over the place will do a good job also, stopping transient transmission of frequencies.
Everything has a natural frequency of oscillation. Metal happens to be particularly good at it. Because of the density. Get the right frequency, and it will hum and sing like a tuning fork.
This is why mounting on the centerline of a vehicle is so much easier. It eliminates multitudes of various lengths of parts that all want to oscillate per the harmonics of the engine and chassis.