A) \[2f\]
B) \[f/2\]
C) \[f/4\]
D) \[4f\]
Correct Answer: A
Solution :
The two springs are in parallel. \[\therefore \] Effective spring constant, \[K={{K}_{1}}+{{K}_{2}}\] Now, frequency of oscillation is given by \[f=\frac{1}{2\pi }\sqrt{\frac{K}{m}}\] or, \[f=\frac{1}{2\pi }\sqrt{\frac{{{K}_{1}}+{{K}_{2}}}{m}}\] ?(i) When both \[{{k}_{1}}\]and \[{{k}_{2}}\] are made four times their original values, the new frequency is given by \[f'=\frac{1}{2\pi }\sqrt{\frac{4{{K}_{1}}+4{{K}_{2}}}{m}}\] \[=\frac{1}{2\pi }\sqrt{\frac{4({{K}_{1}}+4{{K}_{2}})}{m}}=2\left( \frac{1}{2\pi }\sqrt{\frac{{{K}_{1}}+{{K}_{2}}}{m}} \right)\] \[=2f;\] from eqn. (i)You need to login to perform this action.
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