A) \[2\pi \sqrt{\frac{3m}{7k}}\]
B) \[2\pi \sqrt{\frac{7m}{2k}}\]
C) \[3\pi \sqrt{\frac{m}{7k}}\]
D) \[2\pi \sqrt{\frac{3m}{4k}}\]
Correct Answer: C
Solution :
The given system can be redrawn as follows. The above simplification has been done by using series and parallel combinations of springs and the reduced mass concept. In series, \[\frac{1}{{{k}_{eq}}}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\] In parallel, \[{{k}_{eq}}={{k}_{1}}+{{k}_{2}}\] Reduced mass, \[\mu =\frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] Required time period, \[T=2\pi \sqrt{\frac{\mu }{{{k}_{eqe}}}}=2\pi \sqrt{\frac{3m}{4\times 7k/3}}=3\pi \sqrt{\frac{m}{7k}}\]You need to login to perform this action.
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