Two simple harmonic motions are represented by the equations x₁ = 5sin (2π t + π/4) and x₂ = 5√(2)(sin 2π t + cos 2π t). The amplitude of second motion is................ times the amplitude in first motion. Numerical answer type. Work it out, then open the answer.

Answer: 2. A₁ = 5 x₂ = 5√(2)(sin 2π t + cos 2π t) = 5√(2)·√(2)sin (2π t + π/4), so A₂ = 10 (A₂)/(A₁) = 2 So the answer is 2.

Two simple harmonic motions are represented by the equations x₁ =… | JEE Main 2021 (26 Aug, Shift 2)

Q51JEE Main 2021 · 26 AUG · SHIFT 2Medium

Periodic Motion & SHM Basics

Two simple harmonic motions are represented by the equations

$x_1 = 5\sin\left(2\pi t + \frac{\pi}{4}\right)$ and $x_2 = 5\sqrt{2}(\sin 2\pi t + \cos 2\pi t)$ . The amplitude of second motion is ................ times the amplitude in first motion.

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

Show answer and solution

Answer: 2

$A_1 = 5$
$x_2 = 5\sqrt{2}(\sin 2\pi t + \cos 2\pi t) = 5\sqrt{2}\cdot\sqrt{2}\sin\left(2\pi t + \frac{\pi}{4}\right)$ , so $A_2 = 10$
$\frac{A_2}{A_1} = 2$
So the answer is 2.

Report a mistake

Periodic Motion & SHM Basics question from JEE Main 2021 (26 Aug, Shift 2)

More questions on Periodic Motion & SHM Basics