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when two displacements represented by y(...

when two displacements represented by `y_(1) = a sin(omega t)` and `y_(2) = b cos (omega t)` are superimposed the motion is

A

simple harmonic with amplitude `(a)/(b)`

B

simple harmonic with amplitude `sqrt(a^(2)+b^(2))`

C

simple harmonic with amplitude`((a+b))/(2)`

D

not a simple harmonic

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `y_(1)=a sin omegat ` and
`y_(2)=b cos omega t =b sin (omegat+(pi)/(2))`
`A_(1)=a, A_(2)=b, phi=pi//2`j
Since the frequencies of both the displacements are same, resusltant motion will be SHM.
No amplitude `A=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)`.
`:. A=sqrt(a^(2)+b^(2))`
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Knowledge Check

  • When two displacement represented by y_(1) = a sin (omega t) and y_(2) = b cos (omega t) are superimposed, the motion is

    A
    not a simple harmonic
    B
    simple harmonic with amplitude `(a)/(b)`
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    simple harmonic with amplitude `sqrt(a^(2)+b^(2))`
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  • Two wave are represented by equation y_(1) = a sin omega t and y_(2) = a cos omega t the first wave :-

    A
    leads the second by `pi`
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    lags the second by `pi`
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    leads the second by `(pi)/(2)`
    D
    lags the second by `(pi)/(2)`

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