A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2, respectively. Its time period is:
Using the
expressions for velocity for SHM,
v1=ω√A2−x21
v2=ω√A2−x22
Squaring
both,
v21=ω2(A2−x21) ....(3)
v22=ω2(A2−x22) ....(4)
Subtracting (4) from (3), v21−v22=ω2(x22−x21)
⇒4π2(x22−x21)=T2(v21−v22)
⇒T=2π
⎷x22−x21v21−v22 where we have used ω=2πT