A) \[-4\]
B) 4
C) \[4\sqrt{2}\]
D) 8
Correct Answer: C
Solution :
Displacement of the particle is given as \[x=4\,(\cos \pi t+\sin \pi t)\] \[=\frac{4}{\sqrt{2}}\times \sqrt{2}[\cos \pi t+\sin \pi t]\] \[=\left[ \frac{1}{\sqrt{2}}\cos \pi +\frac{1}{\sqrt{2}}\sin \pi t \right]4\sqrt{2}\] \[=\left[ \sin \frac{\pi }{4}\cos \pi t+\cos \frac{\pi }{4}\sin \pi t \right]4\sqrt{2}\] \[x=4\sqrt{2}\sin \left[ \pi t+\frac{\pi }{4} \right]\] \[[\because \sin A\cos B+\cos A\sin B=\sin (A+B)]\] So, amplitude \[=4\sqrt{2}\]You need to login to perform this action.
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