A) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}-{{k}_{2}}}{m}}\]
B) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{m}}\]
C) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]
D) none of the above
Correct Answer: C
Solution :
The two springs in the arrangement form parallel combination. So, spring constant in parallel combination is given by \[k={{k}_{1}}+{{k}_{2}}\] where \[{{k}_{1}}\] and \[{{k}_{2}}\] are force constants of springs. Frequency of oscillation of the system is given by \[n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] or \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]
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