If the amplitudes of a damped harmonic oscillator at times $t=0, t_1$ and $t_2$ are $A_0$, $A_1$ and $A_2$ respectively, then the amplitude of the oscillator at a time of $\left(t_1+t_2\right)$ is

• A

  $\frac{\mathrm{A}_0+\mathrm{A}_1+\mathrm{A}_2}{3}$
• B

  $\frac{\mathrm{A}_2 \mathrm{~A}_0}{\mathrm{~A}_1}$
• C

  $\frac{\mathrm{A}_1 \mathrm{~A}_0}{\mathrm{~A}_2}$
• Correct answer
  D

  $\frac{\mathrm{A}_1 \mathrm{~A}_2}{\mathrm{~A}_0}$

Hence, the correct answer is option: 'D'.