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 in figures. If `(a)/(b)=n^(2)` and `(a)/(R)=n` then the correct equation(s) is (are):

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))`