A) \[\text{s sin }\omega \text{ t}\]
B) \[\text{s }\omega \text{ cos }\omega \text{ t}\]
C) \[\text{s }\omega \text{ sin}\omega \text{t}\]
D) \[-\frac{1}{2}\left( \text{s}{{\omega }^{2}}\text{ sin }\omega \text{t} \right){{\text{t}}^{2}}\]
Correct Answer: A
Solution :
\[a=\frac{{{d}^{2}}x}{d{{t}^{2}}}=-s\omega \sin \omega t.\] On integrating, \[\frac{dx}{dt}=s{{\omega }^{2}}\frac{\cos \omega t}{\omega }=s\sin \omega t\] Again on integrating, we get \[x=s\omega \frac{\sin \omega t}{\omega }=s\sin \omega t\]
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