Question

Two simple harmonic motions are represented by the equations : Y₁ = 10 sin $\left( 3\pi t + \frac{\pi}{4} \right)$and

Y₂ = 5(sin 3πt + $\sqrt{3}$cos 3πt) Their amplitudes are in the ratio of –

• A. 2 : 1
• B. 3 : 1
• C. 1 : 3
• D. 1 : 1

Answer 1

Answer: (D)

1 : 1

Answer 2

Y₁ = 10 sin (3πt + π/4),

Y₂ = 5 × 2 $\left\lbrack \frac{1}{2}\sin 3\pi t + \frac{\sqrt{3}}{2}\cos 3\pi t \right\rbrack$

= 10 sin $\left( 3\pi t + \frac{\pi}{3} \right)$ So, $\frac{A_{1}}{A_{2}}$= 1 : 1