The pendulum is one of the stages of the Destiny 2 Quest for Growth. Completing the quest will earn you the Ruinous Effigy Exotic Trace Rifle, a new Exotic introduced to the game during the Arrivals Season. The pendulum stage is the longest and longest stage and requires visits to four different planets which will all leave the game at the end of the season. Dark Pyramid ships have arrived on every planet, and things are not going well. As such, it's time to milk those areas for one final drop in content before the healing is consigned to Destiny 2's vault.
The pendulum stage is divided into two parts. For the first part, you have to collect 25 fragments of calcified light on Io, Titan, Mars and Mercury. There are five of them on every planet except Io, who has 10, and your ghost will show you where to go if you hold it. We've got a full guide on where to find them, with a map showing all of their locations and videos showing you exactly how to get to each from the nearest spawn point.
You must also find 15 Savathun puppets on Io and Titan. To find them, look in areas that don't have a Contact public event, but you can normally meet at least one during the Contact event if you want to find them that way. You should be able to find plagues, and when you destroy them, taken bosses will appear. Kill them, then a champion will appear. Here is the puppet. While they look a lot like standard champions, you should be able to see "Marionette" on their behalf. Just search in areas with no Contact events, on Io or Titan, and you should run into them on a fairly regular basis.