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In forced oscillation of a particle the ...

In forced oscillation of a particle the amplitude is maximum for a frequency `omega_(2)` of the force while the energy is maximum for a frequecyomega_(2) of the force, then .

A

`omega_(1) lt omega_(2)`

B

`omega_(1) gt omega_(2)`

C

`omega_(1) lt omega_(2)` when damping is small and `omega_(1) gt omega_(2)` when damping is large

D

`omega_(1) = omega_(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`x_(0) = (F//m)/(sqrt((omega_(0)^(2)-omega^(2))^(2)+((b omega)/(m))^(2)))` amplitude is maximum when `omega_(1) = sqrt(omega_(0)^(2)-2 gamma^(2))` and energy is maximum when `omega_(2) = omega_(0)`
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Knowledge Check

  • In forced oscillations , a particle oscillates simple harmonically with a frequency equal to

    A
    frequency of driving force
    B
    natural frequency of body
    C
    differnece of frequency of driving force and natrual frequency
    D
    mean of frequency of driving force and natural frequency

  • A particle, with restoring force proportional to displacement and resulting force proportional to velocity is subjected to a force F sin omega t . If the amplitude of the particle is maximum for omega = omega_(1) , and the energy of the particle is maximum for omega=omega_(2) , then

    A
    `omega_(1) = omega_(0)` and `omega_(2) != omega_(0)`
    B
    `omega_(1) = omega_(0)` and `omega_(2) = omega_(0)`
    C
    `omega_(1) != omega_(0)` and `omega_(2) = omega_(0)`
    D
    `omega_(1) != omega_(0)` and `omega_(2) != omega_(0)`

  • A particle undergoing forced oscillations has maximum amplitude for frequency V_(1) of the force . Then Which of the following statement is true ?

    A
    `V_(1)=V_(2)`
    B
    `V_(1) lt V_(2)`
    C
    `V_(1) gt V_(2)`
    D
    `V_(1)lt V_(2)` when the damping is small and `V_(1) gt V_(2)` when damping is large