How would ones eardrum become perforated if no object was inserted into the ear?

Trauma: External trauma (such as a severe force to the ear or head) as well as very loud noises can perforate the eardum in addition to internal trauma.

From inside to out: Fluid accumulating behind the ear drum when increased to the point of increased pressure may cause a rupture of the ear drum.

Eardrum: Probably due to an infection in the ear that caused this. Most common cause is from using a foreign object to clean ears. Another cause is with intense pressure changes like seen when flying where to ears chart and get blocked sometimes.