A particle performs harmonic oscillation along the \( x \)-axis about the equilibrium position \....

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A particle performs harmonic oscillation along the \( x \)-axis about the equilibrium position \( x=0 \). The oscillation
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frequency is \( \omega=4.00 \mathrm{~s}^{-1} \). At a certain moment of time the particle has a coordinate \( x_{0}=25.0 \mathrm{~cm} \) and its velocity is equal to \( 100 \mathrm{~cm} / \mathrm{s} \)
Find the equation of motion of the particle
(1) \( y=13 \sqrt{3} \sin \left(4 t+\frac{\pi}{4}\right) \)
(2) \( y=25 \sqrt{2} \sin \left(4 t+\frac{\pi}{4}\right) \)
(3) \( y=27 \sqrt{2} \sin \left(4 t+\frac{\pi}{4}\right) \)
(4) \( y=27 \sqrt{5} \sin \left(t+\frac{\pi}{2}\right) \)


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