Find the resulting amplitude and phase of the vibrations
`s=Acosomegat+(A)/(2)cos(omegat+(pi)/(2))+(A)/(4)cos(omegat+pi)+(A)/(8)cos(omegat+(3pi)/(2))`

Answer

`B=(3Asqrt5)/(8)=0.84A;varphi=arc tan""(1)/(2)=0.464" rad "=26.6^(@)`

Explanation

Apply the vector diagram Fig. Here
`B=sqrt((A-(A)/(4))^(2)+(A/(1)-(A)/(8))^(2)),tanvarphi=((A//4)-(A//8))/(A-(A//4))=(1)/(2)`