The displacement of a particle varies according to the relation $x = 3 \sin 100 t + 8 \cos^{2} 50 t$ . Which of the following $is/are$ correct about this motion.

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The amplitude of the resultant SHM is

\sqrt{73}

units

The maximum displacement of the particle from the origin is 9 units

The motion of the particle is not SHM

The amplitude of the SHM of the particle is 5 units

answer is B, D.

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Detailed Solution

3 sin 1 00 t + 8 \frac{[1 + \cos 2 \times 50 \times t]}{2}

$= 3 \sin 100 t + 4 + 4 \cos 100 t$

$= 4 + 3 \sin 100 t + 4 \cos 100 t$

$A = \sqrt{3^{2} + 42} = 5$

4 + 5 = 9 units

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