Two independent equal-mass harmonic oscillators have angular frequencies ω₁, ω₂ and total energies E₁, E₂. Their p–x ellipses are shown. If a/b = n² and a/R = n, choose the correct equation(s).

Question

G1 Physics · Accepted Answer

For a p–x ellipse of an oscillator, pₘₐₓ=mωA. Oscillator 1 has A₁=a and pₘₐₓ=b, so ω₁=b/(ma). Oscillator 2 has A₂=R and pₘₐₓ=R, so ω₂=1/m. Since a/b=n², ω₂/ω₁=a/b=n²: B is true. Also E=pₘₐₓ²/(2m), and using a/R=n with a/b=n² gives E₁/E₂=1/n²=ω₁/ω₂, hence E₁/ω₁=E₂/ω₂: D is true. Correct answers: B, D.