QJEEM21Pheb35: JEE Main 2021 Physics - Class 11 JEEM21Pheb35 Solution: Two simple harmonic motions are represented by the equations x…

Question

Verified Solution • 2025–26 Session moderate

Two simple harmonic motions are represented by the equations

x_{1} = 5 \sin (2 π t + \frac{π}{4})

and

x_{2} = 5 \sqrt{2} (\sin 2 π t + \cos 2 π t)

. The amplitude of second motion is ................ times the amplitude in first motion.

Accepted Answer

x_{2} = 5 \sqrt{2} (\frac{1}{\sqrt{2}} \sin 2 π t + \frac{1}{\sqrt{2}} \cos 2 π t) \sqrt{2}

= 10 \sin (2 π t + \frac{π}{4})

∴

\frac{A_{2}}{A_{1}} = \frac{10}{5} = 2

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