Physics - SHM Question with Solution | TestHub

$\because$Equation of displacement of particle is

$y=4{\cos }^2\left(\frac{t}{2}\right)\sin \left(1000t\right)$.....(i)

Or$y=4\left[\left(\frac{1+\mathrm{c}\mathrm{o}\mathrm{s}t}{2}\right)\mathrm{s}\mathrm{i}\mathrm{n}1000t\right]$

$\left(\because {\cos }^{2}x=\frac{1+\cos 2x}{2}\right)$

Or$y=2\sin 1000t+2\mathrm{c}\mathrm{o}\mathrm{s}t\mathrm{s}\mathrm{i}\mathrm{n}1000t$

Or$y=2 \mathrm{s}\mathrm{i}\mathrm{n}1000t+\mathrm{s}\mathrm{i}\mathrm{n}1001t+\mathrm{s}\mathrm{i}\mathrm{n}t 999t$

$\left[2\sin A\mathrm{c}\mathrm{o}\mathrm{s}B=\sin \left(A+B\right)+\sin \left(A-B\right)\right]$

Hence, equation (i) is the result of the superposition of three simple harmonic motion.