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 a b = n 2 and a R = n , then the correct equation(s) is (are)

Step-by-step solution

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