Two simple harmonic motions are represented by the equations x _ 1 = 5sin (2 + (π)/(4)) and x _ 2 = 5 2 ( 2 + 2 ) . The amplitude of the second motion is _____ times the amplitude in the first motion.

Correct answer: 0 A _ 1 = 5 x _ 2 = 5 2 [ 2 + 2 ] x _ 2 = 10[ (2 + (π)/(4))] A _ 2 = 10 A _ 2 = 2 A _ 1

JEE Main 202126 AugustEvening Shift

JEE Main 2021 · 26 August · Evening Shift · Physics · Oscillations

Two simple harmonic motions are represented by the equations x _ 1...

Two simple harmonic motions are represented by the equations

{x}_{1} = 5sin

\left(2\pit + \dfrac{\pi}{4}\right)

and

{x}_{2} = 5\sqrt{2} ( \sin 2\pit + \cos 2\pit ) . The amplitude of the second motion is _____ times the amplitude in the first motion.

${A}_{1} = 5$

${x}_{2} = 5\sqrt{2} [ \sin 2\pit + \cos 2\pit ]$

${x}_{2} = 10\left[\sin \left(2\piT + \dfrac{\pi}{4}\right)\right]$

${A}_{2} = 10$

${A}_{2} = 2{A}_{1}$