A) \[\frac{4\pi }{3}\]
B) \[\frac{3\,}{8}\pi \]
C) \[\frac{7\,}{3}\pi \]
D) \[\frac{8\,\pi }{3}\]
Correct Answer: D
Solution :
[d] \[v=\omega \sqrt{{{A}^{2}}-{{x}^{2}}}\] |
\[a={{\omega }^{2}}x\] |
\[v=a\] (according to question |
\[\left| velocity \right|\text{ = }\left| acceleration \right|\text{ })\] |
\[~\omega \sqrt{{{A}^{2}}-{{x}^{2}}}\,=\,{{\omega }^{2}}x\] |
\[~\sqrt{{{A}^{2}}-{{x}^{2}}}\,=\,\omega x\] |
\[{{A}^{2}}-{{x}^{2}}={{\omega }^{2}}{{x}^{2}}\] |
\[25-16={{\omega }^{2}}\times 16\] |
\[9={{\omega }^{2}}\times 16\] |
\[\omega \,\,=\,\,\sqrt{\frac{9}{16}}\,\,=\,\frac{3}{4}\] |
\[T\,\,=\,\,\frac{2\pi }{\omega }\,=\,\frac{2\pi }{3}\,\times 4\,\,=\,\,\frac{8\,\pi }{3}\,\sec \] |
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