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A particle is executing SHM along a stra...

A particle is executing SHM along a straight line. Its velocities at distances `x_(1)` and `x_(2)` from the mean position are `v_(1)` and `v_(2)`, respectively. Its time period is

A

`T=2pi sqrt((x_(2)^(2)-x_(1)^(2))/(v_(1)^(2)+v_(2)^(2)))`

B

`T=2pi sqrt((x_(2)^(2)-x_(1)^(2))/(v_(1)^(2)-v_(2)^(2)))`

C

`T=2pi sqrt((x_(2)^(2)+x_(1)^(2))/(v_(1)^(2)+v_(2)^(2)))`

D

`T=2pi sqrt((x_(2)^(2)+x_(1)^(2))/(v_(1)^(2)-v_(2)^(2)))`

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Knowledge Check

  • A particle is performing harmonic motion if its velocity are v_(1) and v_(2) at the displecement from the mean position are y_(1) and y_(2) respectively then its time period is

    A
    ` 2pi sqrt((y_(1)^(2) + y_(2)^(2))/(v_(1)^(2) + v_(2)^(2)))`
    B
    ` 2pi sqrt((v_(2)^(2) - v_(2)^(2))/(y_(1)^(2) - y_(2)^(2)))`
    C
    ` 2pi sqrt((y_(1)^(2) - y_(2)^(2))/(v_(2)^(2) + v_(1)^(2)))`
    D
    ` 2pi sqrt((v_(1)^(2) + v_(2)^(2))/(y_(1)^(2) + y_(2)^(2)))`

  • A particle is executing S.H.M. If u_(1) and u_(2) are the velocitiesof the particle at distances x_(1) and x_(2) from the mean position respectively, then

    A
    `T=2pi sqrt((x_(1)+x_(2))/(u_(1)+u_(2)))`
    B
    `T=2pi sqrt((x_(2)^(2)+x_(1)^(2))/(u_(1)^(2)+u_(2)^(2)))`
    C
    `omega= sqrt((u_(2)^(2) - u_(1)^(2))/(x_(1)^(2) - x_(2)^(2))`
    D
    `2pi sqrt((u_(1)x_(2))/(u_(2)x_(1)))`

  • A particle is vibrating in SHM. If its velocities are v_1 and v_2 when the displacements from the mean postion are y_1 and y_2 , respectively, then its time period is

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    `2pisqrt((y_1^2+y_2^2)/(v_1^2+v_2^2))`
    B
    `2pisqrt((v_1^2+v_2^2)/(y_1^2+y_2^2))`
    C
    `2pisqrt((v_1^2-v_2^2)/(y_1^2-y_2^2))`
    D
    `2pisqrt((y_1^2-y_2^2)/(v_1^2-v_2^2))`

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