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 are particles is same ?

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

Answer 1

Answer: (D)

8 unit

Answer 2

ma = – mg sin θ

a = – g sin θ or a = – g tan θ … (1)

(as θ is small)

Now,

x² = 4ay

∴ $\frac{dy}{dx} = \frac{x}{2a}$

∴ a = – g$\frac{x}{2a}$

– ω²x = – $\frac{gx}{2a}$

ω = $\sqrt{\frac{g}{2a}}$