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A vibratory motion is represented by x=2...

A vibratory motion is represented by `x=2Acosomegat+Acos(omegat+(pi)/(2))+Acos(omegat+pi)+(A)/(2)cos(omegat+(3pi)/(2))`.
the resultant amplitude of the motion is

A

`(9A)/(2)`

B

`(sqrt(5)A)/(2)`

C

`(5A)/(2)`

D

2A

Text Solution

Verified by Experts

The correct Answer is:
B
`x=2Acosomegat+Acos(omegat+(pi)/(2))+Acos(omegat+pi)+(A)/(2)cos(omegat+(3pi)/(2))`
`=2Acosomegat-Asinomegat-Acosomegat+(A)/(2)sinomegat`
`=Acosomegat-(A)/(2)sinomegat`
`therefore`The amplitude of the resultant motion is
`A_(R)=sqrt((A)^(2)+(-(A)/(2))^(2))=(sqrt(5)A)/(2)`
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