Question

A S.H.M. is represented by $x = 5\sqrt{2}(\sin 2\pi t + \cos 2\pi t).$ The amplitude of the S.H.M. is

• A. 10 cm
• B. 20 cm
• C. $5\sqrt{2}$cm
• D. 50 cm

Answer 1

Answer: (A)

10 cm

Answer 2

$x = 5\sqrt{2}\left( \sin 2\pi t + \cos 2\pi t \right)$

$= 5\sqrt{2}\sin 2\pi t + 5\sqrt{2}\cos 2\pi t$

$x = 5\sqrt{2}\sin 2\pi t + 5\sqrt{2}\sin\left( 2\pi t + \frac{\pi}{2} \right)$

Phase difference between constituent waves

$\varphi = \frac{\pi}{2}$

$\therefore$ Resultant amplitude

$A = \sqrt{(5\sqrt{2})^{2} + (5\sqrt{2})^{2}}$=10 cm.