Patrthom is right, it's a resonance. If it didn't happen when new and only recently started then something inside is broken or loose. Could be related to the jack, or it could be something else and when you're touching the wire it happens to dampen the vibration on the case.
If it's under warranty or within the return period that's your best option.
If not then you can try to locate the source of the resonance and apply foam and/or glue as needed. I'd look around particularly small or lightweight parts, given the higher frequency of this resonance. Check the speaker cones, check the tabs and screws that hold the circuit boards down inside the unit, check the power and audio jacks. If anything is loose add a little hot glue or stuff a bit of tissue or foam around it to prevent it from moving.
If that doesn't seem to resolve it then it's possible it's a problem with the amplifier, bad capacitor somewhere for instance, but that's unlikely given the age and difficult to diagnose and fix without test equipment and a decent technician.