A particle of unit mass performing (lightly) damped simple harmonic oscillations satisﬁes the above equation of motion x¨ + 2γx˙ + ω0^2x = 0), The three consecutive positions of its instantaneous rest, relative to an
arbitrary origin O, are given by x = a1, x = a2, x = a3.

If in three consecutive positions of instantaneous rest the particle is at x = 6, x = 3, x = 4
at approximately equal intervals of 2 seconds, show, using the expression x0=a1a3 - a2^2 / a1-2a2+a3)) that the period
of oscillations for the undamped oscillator would have been
T= 4π/ root( π^2 +( ln3)^2)

Question

A particle of unit mass performing (lightly) damped simple harmonic oscillations satisﬁes the above equation of motion x¨ + 2γx˙ + ω0^2x = 0), The three consecutive positions of its instantaneous rest, relative to an
arbitrary origin O, are given by x = a1, x = a2, x = a3.

If in three consecutive positions of instantaneous rest the particle is at x = 6, x = 3, x = 4
at approximately equal intervals of 2 seconds, show, using the expression x0=a1a3 - a2^2 / a1-2a2+a3)) that the period
of oscillations for the undamped oscillator would have been
T= 4π/ root( π^2 +( ln3)^2)