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Two simple harmonic motions are given by...

Two simple harmonic motions are given by `x_(1) = a sin omega t + a cos omega t and x_(2) = a sin omega t + (a)/(sqrt3) cos omega t`
The ratio of the amplitudes of first and second motion and the phase difference between them are respectively

A

`sqrt((3)/(2)) and (pi)/(12)`

B

`(sqrt3)/(2) and (pi)/(12)`

C

`(2)/(sqrt3) and (pi)/(12)`

D

`sqrt((3)/(2)) and (pi)/(6)`

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Knowledge Check

  • Two simple harmonic motions are given by x_1 = asinomegat and x_2 = asinomegat + a/sqrt3 cosomegat . The ratio of the amplitudes of first and phase difference between them are respectively.

    A
    `sqrt(3/2)` and `(pi)/12`
    B
    `sqrt(3)/2` and `(pi)/12`
    C
    `2/sqrt(3)` and `(pi)/12`
    D
    `sqrt(3/2)` and `(pi)/6`

  • When the waves y_(1) = A sin omega t and y_(2) = A cos omega t are superposed, then resultant amplitude will be

    A
    `sqrt(2) ` A
    B
    `(1)/(sqrt(2))A`
    C
    A
    D
    2A

  • If two waves represented by y_(1) =4 sin omega t and y_(2)=3"sin" (omega+(pi)/(3)) interfere at a point the amplitude of the resulting wave will about

    A
    7
    B
    6
    C
    5
    D
    3.5

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