Technically it is called "HUNTING" which means it is hunting to maintain the SET Pressure and it more like a chattering sound then hydraulic shock (water hammer)
A surge in water pressure can cause this. Also, a defective ballcock would pop off under these conditions. Replace the ballcock and consider installing a pressure reducing valve (PRV) on the incoming water line.
Incorrect filter, defective filter, weak oil pump, clogged oil pump strainer, clogged oil galleys, worn engine bearings, defective oil pressure gage, or defective oil pressure sending unit.
If the engine fan is working then you could have a defective thermostat or a blown head gasket.
Low refrigerant defective pressure switch
Steam? Leak? overheating due to low coolant? Back pressure due to a bad thermostat? Defective radiator cap? have system pressure tested to determine location of leak
D. hammering it into a new shape
Water hammer in plumbing systems is caused by the sudden stoppage or change in direction of water flow, leading to a pressure surge that creates a banging or hammering noise in the pipes.
The oil pressure sending unit is defective.
Out of gas, blown fuel pump fuse, bad fuel pump, bad fuel pump relay, clogged fuel filter, loose or corroded wiring, defective fuel pressure regulator, or in rare instances a defective computer.
Worn crankshaft bearings, oil pump, or a defective oil pressure sending unit. Have a oil pressure test done with a mechanical gauge, the electric gauge is not very accurate and is prone too failure.
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The defective sway bar link can cause the clunking or the rattling of the noise from the front suspension during the low speed driving.