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  4. The displacement of a particle varies according to the relation x=3 sin 100 t+8 cos 2 50 t. The amplitude of the resultant SHM is y units. Find y.

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Q. The displacement of a particle varies according to the relation $x=3 \sin 100 t+8 \cos ^{2} 50\, t$. The amplitude of the resultant SHM is $y$ units. Find $y$.

Oscillations

Solution:

$x=3 \sin 100\, t+8 \cos ^{2} 50 t$
$=3 \sin 100\, t+8\left(\frac{1+\cos 2 \times 50 t}{2}\right)$
$=3 \sin 100 \,t+4 \cos 100\, t+4$
$x=5 \sin (100 \,t)+4$
$ \Rightarrow A=5$