Here the two balls connected by the springs are free to oscillate along the length of the springs, so the time period will depend on the reduced mass of the two-ball system.
(a) Restoring force on A or B
Where ∆x is compression in the spring at one end?
Effective force constant = 2k
Where µ is reduced mass of system.
(b) P and Q are equilibrium position. Balls A and B at P and Q have only kinetic energy and it is equal the potential energy at extreme positions.
Potential energy at extreme position
When the balls A and B are at points P and Q respectively
(c) Total potential and kinetic energy of the system is equal to total potential energy at the extreme position=3.94 x 10-4J.