Question

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. `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 1

Correct Answer - B::D
For forst oscillator `E_(1) = (1)/(2) m omega_(1)^(2)a^(2)`, and `p = mv = m omega_(1)a = b rArr (a)/(b) = (1)/(m omega_(1)) …….(i)`
for second oscillator
`E_(2) = (1)/(2) m omega_(2)^(2) R^(2)`, and `m omega_(2) = 1………….(ii)`
`((a)/(b)) = (omega_(2))/(omega_(1) =n^(2))`
`(E_(1))/(omega_(1)^(2)a^(2))= (E_(2))/(omega_(2)^(2)R^(2)) rArr (E_(1))/(omega_(1)) = (E_(2))/(omega_(2))`