A) \[{{\left( \frac{{{k}_{1}}}{{{k}_{2}}} \right)}^{1/2}}\]
B) \[{{\left( \frac{{{k}_{2}}}{{{k}_{1}}} \right)}^{1/2}}\]
C) \[\frac{{{k}_{1}}}{{{k}_{2}}}\]
D) \[\frac{{{k}_{2}}}{{{k}_{1}}}\]
Correct Answer: B
Solution :
As, \[\omega =\sqrt{\frac{k}{m}}\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\omega \propto \sqrt{k}\] Hence, the angular frequency is directly proportional to the square root of spring constant and \[\operatorname{maximum} velocity =A\omega \,(A\,\,is amplitude)\] Now for equal maximum velocity \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}\] \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{\omega }_{2}}}{{{\omega }_{1}}}=\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}={{\left( \frac{{{k}_{2}}}{{{k}_{1}}} \right)}^{1/2}}\]
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