Let the amplitude of the oscillation beAandωbe the angular frequency then,
v21=ω2(A2−x21)
v22=ω2(A2−x22)
EliminatingAfrom the above equations by subtracting we get
ω2=(v21−v22x22−x21)
We know
ω=2πT
T=2π√(x22−x21v21−v22)
Hence, the time period is T=2π ⎷(x22−x21v21−v22)