Home
Class 12
PHYSICS
Two independent harmonic oscillators of ...

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##)

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))`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`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))`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Match The Column|9 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Paragraph|3 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise-05 [B]|12 Videos

  • RACE

    ALLEN|Exercise Basic Maths (Wave Motion & Dopplers Effect) (Stationary waves & doppler effect, beats)|25 Videos

  • TEST PAPER

    ALLEN|Exercise PHYSICS|4 Videos

Similar Questions

Explore conceptually related problems

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) repsectively. The variations of their momenta p with positions x are shown in figures. If (a)/(b) = n^(2) and (a)/(R) = n , then the correc t equation(s) is (are) :

Two bodies of different masses m_(1) and m_(2) have equal momenta. Their kinetic energies E_(1) and E_(2) are in the ratio

The forced harmonic oscillations have equal displacement amplitude at frequencies omega_(1)=400 s^(-1) and omega_(2)=600 s^(-1) . Find the resonance frequency at which the displacement amplitude is maximum.

Two physical pendulums perform small oscillations about the same horizontal axis with frequencies omega_(1) and omega_(2) . Their moments of inertia relative to the given axis are equal to I_(1) and I_(2) respectively. In a state of stable equilibium the pendulums were fastened rigifly together. What will be the frequency of small oscillations of the compound pendulum ?

Find the angular frequency and the amplitude of harmonic oscillations of a particle if at distances x_(1) and x_(2) from the equalibrium position its velocity equald v_(1) and v_(2) respectively.

A particle of mass m = 1 kg excutes SHM about mean position O with angular frequency omega = 1.0 rad//s and total energy 2J . x is positive if measured towards right from O . At t = 0 , particle is at O and movel towards right.

Two bodies of masses m and 2m have same momentum. Their respective kinetic energies E_(1 ) and E_(2) are in the ratio

A particle performing SHM with angular frequency omega=5000 radian/second and amplitude A=2 cm and mass of 1 kg. Find the total energy of oscillation.

Two discs of moments of inertia I_1 and I_2 about their respective axes, rotating with angular frequencies, omega_1 and omega_2 respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be A .