MCQ
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 .... $cm$
- ✓$10$
- B$20$
- C$5\sqrt 2 $
- D$50$
✓
Answer
Correct option: A.
$10$
a
(a) $x = 5\sqrt 2 \left( {\sin 2\pi \,t + \cos 2\pi \,t} \right)$
$ = 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 $\phi = \frac{\pi }{2}$
$\therefore $ Resultant amplitude $A = \sqrt {{{(5\sqrt 2 )}^2} + {{(5\sqrt 2 )}^2}} \,=10 \,cm.$
(a) $x = 5\sqrt 2 \left( {\sin 2\pi \,t + \cos 2\pi \,t} \right)$
$ = 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 $\phi = \frac{\pi }{2}$
$\therefore $ Resultant amplitude $A = \sqrt {{{(5\sqrt 2 )}^2} + {{(5\sqrt 2 )}^2}} \,=10 \,cm.$
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