Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$ and have total energies ${\mathrm{E}}_1$ and ${\mathrm{E}}_2$ , respectively. The variations of their momenta $\mathrm{p}$ with positions $\mathrm{x}$ are shown in the figures. If $\frac{\mathrm{a}}{\mathrm{b}}={\mathrm{n}}^2$ and $\frac{\mathrm{a}}{\mathrm{R}}=\mathrm{n}$ , then the correct equation(s) is (are)

• A

  ${\mathrm{E}}_1{\mathrm{\omega }}_1={\mathrm{E}}_2{\mathrm{\omega }}_2$
• Correct answer
  B

  $\frac{{\mathrm{\omega }}_2}{{\mathrm{\omega }}_1}={\mathrm{n}}^2$
• C

  ${\mathrm{\omega }}_1{\mathrm{\omega }}_2={\mathrm{n}}^2$
• Correct answer
  D

  $\frac{{\mathrm{E}}_1}{{\mathrm{\omega }}_1}=\frac{{\mathrm{E}}_2}{{\mathrm{\omega }}_2}$

Hence, the correct answer is options: 'B', 'D'.