Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies ω 1 and ω 2 and have total energies E 1 and E 2 , respectively. The variations of their mom

Question

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $ω_{1}$ and $ω_{2}$ and have total energies $E_{1}$ and $E_{2}$ , respectively. The variations of their momenta $p$ with positions $x$ are shown in the figures. If $\frac{a}{b} = n^{2}$ and $\frac{a}{R} = n$ , then the correct equation(s) is (are)

TestHub · Accepted Answer

P 1 m a x = m a ω 1 = b P 2 m a x = m r ω 2 = R ω 1 ω 2 = 1 n 2 ω 2 ω 1 = n 2 E 1 = 1 2 m ω 1 2 a 2 E 2 = 1 2 m ω 2 2 R 2 E 1 E 2 = ω 1 2 ω 2 2 a 2 R 2 = ω 1 2 ω 2 2 n 2 = ω 1 2 ω 2 2 ω 2 ω 1 E 1 E 2 = ω 1 ω 2 E 1 ω 1 = E 2 ω 2

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