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  4. The equation of motion of a particle executing SHM is, α +16π 2x=0. In this equation α is the linear acceleration in m/s2, of the particle at a displacement x metre. The time period of SHM, in second, is:

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Q. The equation of motion of a particle executing SHM is, $ \alpha +16{{\pi }^{2}}x=0. $ In this equation $ \alpha $ is the linear acceleration in $ m/{{s}^{2}}, $ of the particle at a displacement x metre. The time period of SHM, in second, is:

EAMCETEAMCET 2004

Solution:

The equation of motion and particles executing SHM is given by $ \alpha +16{{\pi }^{2}}x=0 $ $ \alpha =-16{{\pi }^{2}}x $ But from the relation in SHM, acceleration is given by $ \alpha =-{{\omega }^{2}}x $ So, $ -{{\omega }^{2}}x=-16{{\pi }^{2}}x $ or $ \omega =4\pi $ $ \,\,\,(\because \omega =2\frac{\pi }{T}) $ or $ \frac{2\pi }{T}=4\pi $ Hence, $ T=\frac{1}{2}s $