Four simple harmonic vibrations x1=8  sin wt, x2=6sin(wt+π/2),x3=4sin(wt+π)  and x4=2sin(ωt+3π2)  are superimposed on each other. The resulting amplitude is

Given x1=8sinωt , x2=6sin(ωt+π2) x3=4sin(ωt+π) and x4=2sin(ωt+3π2) From super position principle application displacement x=x1+x2+x3+x4 x=8sinωt+6sin(ωt+π2)+4sin(ωt+π)+2sin(ωt+3π2) x=8sinωt+6cosωt−4sinωt−2cosωt x=4sinωt+4cosωt x=4(sinωt+cosωt) x=4((2sinωtcosπ4)+(2cosωtsinπ4)) x=42(sinωtcosπ4)+(cosωtsinπ4) SinACosB+CosASinB=Sin(A+B) ∴x=42sin(ωt+π4) ∴ The resulting amplitude =42