Question

The displacement of two identical particles executing SHM are represented by equations x₁ = 4 sin $\left( 10t + \frac{\pi}{6} \right)$ and

x₂ = 5 cosωt. For what value of ω energy of both the particles is same ?

• A. 16 unit
• B. 6 unit
• C. 4 unit
• D. 8 unit

Answer 1

Answer: (D)

8 unit

Answer 2

E₁ = E₂

∴ $\frac { 1 } { 2 }$ $m_{1}$ $\frac { 1 } { 2 }$ $m_{2}$ $\omega _ { 2 } ^ { 2 }$ $A_{2}^{2}$

but m₁ = m₂

∴ $\omega_{1}^{2}$ × 16 = $\omega_{2}^{2}$ × 25

∴ 100 × 16 = ω² × 25

ω = 8 units