A) \[t={{t}_{1}}+{{t}_{2}}\]
B) \[t=\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
C) \[{{t}^{2}}=t_{1}^{2}+t_{2}^{2}\]
D) \[{{t}^{-2}}=t_{1}^{-2}+t_{2}^{-2}\]
Correct Answer: D
Solution :
\[{{t}_{1}}=2\pi \sqrt{\frac{m}{{{K}_{1}}}}\]and \[{{t}_{2}}=2\pi \sqrt{\frac{m}{{{K}_{2}}}}\] Equivalent spring constant for shown combination is \[{{K}_{1}}+{{K}_{2}}.\]So time period t is given by \[t=2\pi \sqrt{\frac{m}{{{K}_{1}}+{{K}_{2}}}}\] By solving these equations we get \[{{t}^{-2}}={{t}_{1}}^{-2}+{{t}_{2}}^{-2}\]
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