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Four simple harmonic vibrations x(1) =...

Four simple harmonic vibrations
`x_(1) = 8s "in" (omegat), x_(2) = 6 sin (omegat +(pi)/(2))`,
`x_(3) = 4 sin (omegat +pi)` and `x_(4) =2 sin (omegat +(3pi)/(2))` are superimposed on each other. The resulting amplitude is……units.

A

`20`

B

`8sqrt(2)`

C

`4sqrt(2)`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
C
`A_(res) = sqrt((A_(1)-A_(3))^(2)+(A_(1)-A_(4))^(2))`
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Knowledge Check

  • Four simple harmonic motions , c_(1)=8sinomegat,x_(2)=6sin(omegat=pi//2) , x_(3)=4sin(omegat+pi) and x_(4)=2sin (omegat+3pi//2) are superimposed on each other. The resuslting amplitude and its phase difference with x_(1) are respectively

    A
    `20, tan^(-1)(1//2)`
    B
    `4sqrt(2), pi//2`
    C
    `20, tan^(-1)(2)`
    D
    `4sqrt(2), pi//4`

  • Four simple harmonic vibrations x_(1) = 8sinepsilont , x_(2) = 6sin(epsilont+pi/2) , x_(3)=4sin(epsilont_pi) and x_(4) = 2sin(epsilon+(3pi)/2) are superimposed on each other. The resulting amplitude and its phase difference with x_(1) are respectively.

    A
    `20, tan^(-1)(1/2)`
    B
    `4sqrt(2),pi/2`
    C
    `20, tan^(-1)(2)`
    D
    `4sqrt(2),pi/4`

  • For simple harmonic vibrations y_(1)=8cos omegat y_(2)=4 cos (omegat+(pi)/(2)) y_(3)=2cos (omegat+pi) y_(4)=cos(omegat+(3pi)/(2)) are superimposed on one another. The resulting amplitude and phase are respectively

    A
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    B
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    C
    `sqrt(75) and tan^(-1)(2)`
    D
    `sqrt(75) and tan^(-1)((1)/(3))`