1.

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 isA. `(9A)/(2)`B. `(sqrt(5)A)/(2)`C. `(5A)/(2)`D. 2A

Answer» Correct Answer - 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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