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  4. The position of a particle with respect to origin varies according to the relation x=3 sin 100 t+8 cos 2 50 t. The maximum displacement of the particle from the origin is

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Q. The position of a particle with respect to origin varies according to the relation $x=3 \sin 100 t+8 \cos ^{2} 50 t$. The maximum displacement of the particle from the origin is ____

Oscillations

Solution:

$x=3 \sin 100 t+8 \cos ^{2} 50 t$
$=3 \sin 100 t+\frac{8[1+\cos 100 t]}{2}$
$x=4+3 \sin 100 t+4 \cos 100 t$
$(x-4)=5 \sin (100 t+\phi)\left\{\tan \phi=\frac{4}{3}\right\}$
Amplitude $=5$ units
Maximum displacement $=9$ units