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  4. An SHM is given by y = 5 [ sin (3 π t) + √3 cos (3 π t)] What is the amplitude of the motion of y in metre?

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Q. An SHM is given by $y = 5 [\sin (3 \pi t) + \sqrt{3} \cos (3 \pi t)] $ What is the amplitude of the motion of $y$ in metre?

Haryana PMTHaryana PMT 2011

Solution:

Given equation is $y=5[\sin 3 \pi t+\sqrt{3 \cos 3 \pi t}]$
or $y=5 \times 2\left[\sin 3 \pi t \times \frac{1}{2}=\frac{\sqrt{3}}{2} \cos 3 \pi t\right]$
or $y=10 \sin \left(3 \pi t \frac{\pi}{3}\right)$