Two SHMs are x₁ = 5 sin(2πt + π/4) and x₂ = 5√2[sin(2πt) + cos(2πt)]. The amplitude of the second motion is times the amplitude of the first.
Physics · Simple Harmonic Motion
JEE Mains 2021

Question

Two SHMs are x₁ = 5 sin(2πt + π/4) and x₂ = 5√2[sin(2πt) + cos(2πt)]. The amplitude of the second motion is times the amplitude of the first.

G1 Physics · Accepted Answer

First SHM amplitude is 5. For x₂=5√2[sin2πt+cos2πt], bracket amplitude is √2, so total amplitude is 5√2·√2=10. Ratio second/first=10/5=2. Required answer: 2.