most probably it is the McPherson struts ie the shocks that are gone - I have had the same in other cars with McPherson and it is most annoying - does not happen at higher speed as you get away from the natural frequency of the "shot shock"

how does car go on the bounce test at front?

if never replaced shocks then I would do it now [back as well] - car will drive heaps better

 

Also look at the rubber carrier under the car for the driveshaft.