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).
(##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

For first oscillarator , For second oscillator
`b = maomega_(1)`
`(a)/(b) = (1)/(momega_(1)) = n^(2) , (1)/(momega_(2)) = 1`
`(omega_(2))/(omega_(1)) = n^(2)`
`E_(1) = (1)/(2)m omega_(1)^(2) a^(2) , E_(3) = (1)/(2)momega_(2)^(2) R^(2)`
`(E_(1))/(E_(2)) = (omega_(1)^(2))/(omega_(2)^(2)) xx n^(2) = (omega_(1)^(2))/(omega_(2)^(2)) xx (omega_(2))/(omega_(1)) , (E_(1))/(E_(2)) = (omega_(1))/(omega_(2)) rArr (E_(1))/(omega_(1)) = (E_(2))/(omega_(2))`