A) \[\sqrt{{{k}_{1}}/{{k}_{2}}}\]
B) \[{{k}_{1}}/{{k}_{2}}\]
C) \[\sqrt{{{k}_{2}}/{{k}_{1}}}\]
D) \[{{k}_{2}}/{{k}_{1}}\] \[\]
Correct Answer: C
Solution :
The maximum velocity, \[{{v}_{\max }}=a\omega =a\frac{2\pi }{T}\] \[=\frac{2\pi a}{2\pi \sqrt{\frac{m}{k}}}=a\sqrt{\frac{k}{m}}\] where, A is amplitude and T is time period. Hence, \[\frac{{{v}_{{{\max }_{1}}}}}{{{v}_{{{\max }_{2}}}}}=\frac{{{a}_{1}}}{{{a}_{2}}}\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\] \[\because \] \[{{v}_{{{\max }_{1}}}}={{v}_{{{\max }_{2}}}}\] (given) \[\frac{{{a}_{1}}}{{{a}_{2}}}=\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}\]
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