Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies `(omega_1) and (omega_2) and have total energies (E_1 and E_2), respectively. The variations of their momenta (p) with positions (x) are shown (s) is (are) a/b = n(square) and a/R= n, then the correct eqution......
(##JMA_CHMO_C10_022_Q01##)

Options

A. `E_(1)omega_(1) = E_(2)omega_(2)`
B. `(omega_(2))/(omega_(1)) = n^(2)`
C. `omega_(1)omega_(2) = n^(2)`
D. `(E_(1))/(omega_(1)) = (E_(2))/(omega_(2))`

Answer

B, D

Explanation

`P_(1max) = maomega_(1) = b`
`P_(2max) = mRomega_(2) = R`
`(omega_(1))/(omega_(2)) = (1)/(n^(2))`
`(omega_(2))/(omega_(1)) = n^(2)`
`E_(1) = 1/(2)momega_(1)^(2)a^(2)`
`E_(2) = (1)/(2)momega_(2)^(2)R^(2)`
`(E_(1))/(E_(2)) = (omega_(1)^(2))/(omega_(2)^(2)) (a^(2))/(R^(2)) = (omega_(1)^(2))/(omega_(2)^(2)) n^(2) = (omega_(1)^(2))/(omega_(2)^(2)) (omega_(2))/(omega_(1))`
`(E_(1))/(E_(2)) = (omega_(1))/(omega_(2))`
`(E_(1))/(E_(2)) = (E_(2))/(omega_(2))`