Drilling oscillation systems and shock tools for same

A shock tool for reciprocating a drillstring includes an outer housing. The outer housing has a central axis, a first end, a second end opposite the first end, and a passage extending axially from the first end to the second end. In addition, the shock tool includes a mandrel assembly coaxially disposed in the passage of the outer housing and configured to move axially relative to the outer housing. The mandrel assembly has a first end axially spaced from the outer housing, a second end disposed in the outer housing, and a passage extending axially from the first end of the mandrel assembly to the second end of the mandrel assembly. The mandrel assembly includes a mandrel and a first annular piston fixably coupled to the mandrel. The first annular piston is disposed at the second end of the mandrel assembly and sealingly engages the outer housing.