Question Detail
Question
The equation for displacement of two identical particles performing S.H.M. is given by y₁ = 4 sin(20t + π/6) and y₂ = 10 sin(ωt). For what value of ω will both particles have the same energy?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The total energy of a particle in SHM is E = ½mω²A². For identical particles (same mass), the energies are equal when ω₁²A₁² = ω₂²A₂². For particle 1: A₁ = 4, ω₁ = 20. For particle 2: A₂ = 10, ω₂ = ω. So (20²)(4²) = (ω²)(10²) => 400 × 16 = 100ω² => 6400 = 100ω² => ω² = 64 => ω = 8.
Hint
Energy in SHM is proportional to ω²A². Set the energies equal for the two particles.