A “zinging noise” is probably the starter gear not quite meshing with the flywheel’s ring gear. First make sure the battery is fully charged and does not sag too much under load. Many of these small engines don’t use a solenoid, instead they have a bendix gear that uses inertia to accomplish the same task. These types of starters are very sensitive to weak batteries. I would even try jumping it from a running car.
If that doesn’t help, the next step is to turn the engine by hand about a quarter turn, then try the starter. This is to check the ring gear, most engines will always stop at the same place, so the starter usually hits the ring gear in that one place. Rotating the crank a few degrees exposes newer gear teeth to the starter. If that gets the starter to engage, or engage for most of a turn and then resume zinging, you need to replace the ring gear on the flywheel (or get used to turning it by hand a bit before hitting the starter).
If you made it this far and haven’t found the problem yet, pull the starter and either replace or repair it.