"Let me hear your balalaika's ringing out" (where "ringing out" is a gerund and "balalaika" [singular] is a possessive noun)
"Let me hear your balalaikas' ringing out" (where "ringing out" is a gerund and "balalaikas" [plural] is a possessive noun)
"Let me hear your balalaikas ringing out" (where "ringing out" is a participle modifying "balalaikas," which is the direct object of "hear")