A) \[\frac{{{k}_{1}}}{{{k}_{2}}}\]
B) \[\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\]
C) \[\frac{{{k}_{2}}}{{{k}_{1}}}\]
D) \[\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}\]
Correct Answer: D
Solution :
Maximum velocity of SHM (or spring-mass motion) can be given by \[{{v}_{\max }}=A\,\omega \] As \[\omega =\sqrt{\frac{k}{m}}\] \[{{v}_{\max }}=A\sqrt{\frac{k}{m}}\] Given, \[{{v}_{1\,(\max )}}={{v}_{2(\max )}}\] and \[{{m}_{1}}={{m}_{2}}\] \[\therefore \] \[{{A}_{1}}\sqrt{\frac{{{k}_{1}}}{m}}={{A}_{2}}\sqrt{\frac{{{k}_{2}}}{m}}\] \[\Rightarrow \] \[\frac{{{A}_{1}}}{{{A}_{2}}}=\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\]You need to login to perform this action.
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