Riding over obstacles with a regular motorcycle is not usually a problem. The suspension and bike setup on most modern street motorcycles allows for a smooth transition over all but the largest obstacles.
Think about the recommended Motorcycle Safety Foundation procedure for crossing a 2×4 in the road or hitting a “pothole” that is 2″ or so deep… you should try to cross at or near a 90-degree angle, stand up on the foot pegs to use your legs as shock absorbers, roll on the throttle a little to lighten the front-end as you cross the obstacle (and rolling off as you cross it to avoid throwing the obstacle up behind you), clear over the obstacle, and ride on.
With a chopper the procedure is slightly different. The greater than normal rake, extended front forks, far-forward controls, minimal (if any) rear shock travel, and low ground clearance requires more faith and strength and will take some practice to be able to complete the procedure safely. Of course, the best course of action is avoid obstacles completely (they say chopper riders are the most vigilant road surface scanners) but that just isn’t realistic on today’s...