When two displacements represented by y₁ = a sin(ωt) and y₂ = b cos(ωt) are superimposed, the motion is:
Options

Question

When two displacements represented by y₁ = a sin(ωt) and y₂ = b cos(ωt) are superimposed, the motion is:

G1 Physics · Accepted Answer

Step 1: Resultant displacement: y = a sin(ωt) + b cos(ωt). Step 2: Sine and cosine of the same frequency combine into a single sinusoid: y = R sin(ωt + φ). Step 3: By coefficient comparison, R² = a² + b². Step 4: The resultant is SHM of amplitude √(a² + b²). Final answer: (C) simple harmonic with amplitude √(a² + b²).