What did they do during Apollo 13?

Answer 1

The mission began with a little-known smaller incident: during the second-stage boost, the center (inboard) engine shut down two minutes early. The four outboard engines burned longer to compensate, and the vehicle continued to a successful orbit.[7] The shutdown was determined to be due to dangerous pogo oscillations that threatened to tear the second stage apart. The engine experienced 68gvibrations at 16 hertz, flexing the thrust frame by 3 inches (76 mm). The engine shutdown was triggered by sensed thrust chamber pressure fluctuations. Smaller pogo oscillations had been seen on previous Titan and Saturn flights (notably Apollo 6),[8] but on Apollo 13 they were amplified by an unexpected interaction with turbopump cavitation.[9] Later missions implemented anti-pogo modifications that had been under development. These included addition of a helium gas reservoir to the center engine liquid oxygen line to dampen pressure oscillations, an automatic cutoff as a backup, and simplification of the propellant valves of all five second-stage engines.

En route to the Moon, approximately 200,000 miles (320,000 km) from Earth,Mission Control asked Swigert to turn on the hydrogen and oxygen tank stirring fans, which were designed to destratify the cryogenic contents and increase the accuracy of their quantity readings. Approximately 93 seconds later, just under 56 hours since launch, the astronauts heard a "loud bang", accompanied by fluctuations in electrical power and firing of the attitude control thrusters.[6] The crew initially thought that a meteoroid might have struck the Lunar Module (LM).

In fact, the number 2 oxygen tank, one of two in the Service Module (SM), had exploded.[10]Damaged Teflon insulation on the wires to the stirring fan inside oxygen tank 2 allowed the wires to short-circuit and ignite this insulation. The resulting fire rapidly increased pressure beyond its 1,000 pounds per square inch (6.9 MPa) limit and the tank dome failed, filling the fuel cell bay (Sector 4) with rapidly expanding gaseous oxygen and combustion products. It is also possible some combustion occurred of the Mylar/Kapton thermal insulation material used to line the oxygen shelf compartment in this bay.13-foot Sector 4 outer aluminum skin panel, which as it blew off probably caused minor damage to the nearby high-gain S-band antenna used for translunar communications. Communications and telemetry to Earth were lost for 1.8 seconds, until the system automatically corrected by switching the antenna from narrow-band to wide-band mode.