Find length of spring A in equilibrium position

[ally2106]

As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When the piston is pinned to the wall, the lengths of the springs are LA1 = 0.1 and LB1 = 0.1 (in m), respectively. Both springs possesses dissipative properties so that after the pin is pulled, the piston eventually comes to rest at an equilibrium position. Find the length of spring A in this equilibrium position (LA2) in units of m.

Equations so far:
Models:
Elastic Energy Constituitive Relation: (E₂ - E₁) = (k/2)(x₂² - x₁²)

First Law of thermodynamics: (E₂ - E₁) = (Q_1-2) - (W_1-2)
Second Law of thermodynamics...

Don't really know where to start? Help appreciated

 

[BvU]

Hello Ally, welcome to PF !

You bring in thermodynamics, but is that really intended for this exercise ? I don't see any other given than "vacuum" , so I must assume that applies to both volume A and volume B. And then the exercise becomes a simple force balance.