Question

The equation for displacement of two identical particles performing S.H.M. is given by x₁ = 4 sin (20t + p/6) and x₂ = 10 sin ωt. For what value of u will both particles have same energy?

(A) 4 units 

(B) 8 units 

(C) 16 units 

(D) 20 units

Answer 1

The correct option (B) 8 units

Explanation:

Total energy = (1/2) mω² A²

i.e.

E ∝ ω² A²              (1)

given: x₁ = 4 sin {20t + (π / 6)}

x₂ = 10 sin ωt

∴ A₁ = 4, ω₁ = 20, A₂ = 10, ω₂ = ω

for both particles to have same energy, from (1)

(A₁ ω₁)² = (A₂ ω₂)²

∴ (4 × 20)² = (10 × ω)²

∴ 80 = 10ω i.e. ω = 8 units