Two SHMs are y₁ = 10 sin(3πt + π/3) and y₂ = 5[sin(3πt) + √3 cos(3πt)]. If amplitude ratio y₁:y₂ = x:1, find x.
Physics · Simple Harmonic Motion
JEE Mains 2021

Question

Two SHMs are y₁ = 10 sin(3πt + π/3) and y₂ = 5[sin(3πt) + √3 cos(3πt)]. If amplitude ratio y₁:y₂ = x:1, find x.

G1 Physics · Accepted Answer

For y₁, amplitude is 10. For y₂=5[sin3πt+√3 cos3πt], amplitude=5√(1+3)=10. Thus amplitude ratio y₁:y₂=1:1, so x=1.