Two simple harmonic motion, are represented by the equations y₁ = 10sin (3π t + π/3) y₂ = 5(sin 3π t + √(3)cos 3π t) Ratio of amplitude of y1 to y2 = x: 1. The value of x is ______________. Numerical answer type. Work it out, then open the answer.

Answer: 1. A₁ = 10 y₂ = 5(sin 3π t + √(3)cos 3π t) = 10sin (3π t + π/3), so A₂ = 5√(1 + 3) = 10 (A₁)/(A₂) = 1 So x = 1.

Two simple harmonic motion, are represented by the equations y₁ =… | JEE Main 2021 (27 Aug, Shift 2)

Q50JEE Main 2021 · 27 AUG · SHIFT 2Medium

Periodic Motion & SHM Basics

Two simple harmonic motion, are represented by the equations $y_1 = 10\sin\left(3\pi t + \frac{\pi}{3}\right) \quad y_2 = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t)$ Ratio of amplitude of y1 to y2 = x: 1. The value of x is ______________.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

$A_1 = 10$
$y_2 = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t) = 10\sin\left(3\pi t + \frac{\pi}{3}\right)$ , so $A_2 = 5\sqrt{1 + 3} = 10$
$\frac{A_1}{A_2} = 1$
So $x = 1$ .

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