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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

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  • 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

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