A mass m is suspended from the two coupled springs connected in series. The force constant for springs are \[{{K}_{1}}\] and \[{{K}_{2}}\]. The time period of the suspended mass will be [CBSE PMT 1990; Pb. PET 2002]

\[T=2\pi \sqrt{\left( \frac{m{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)}\]

\[T=2\pi \sqrt{\left( \frac{m}{{{K}_{1}}+{{K}_{2}}} \right)}\]

\[T=2\pi \sqrt{\left( \frac{m({{K}_{1}}+{{K}_{2}})}{{{K}_{1}}{{K}_{2}}} \right)}\]

A mass m is suspended from the two coupled springs connected in series

1.	A mass m is suspended from the two coupled springs connected in series. The force constant for springs are \[{{K}_{1}}\] and \[{{K}_{2}}\]. The time period of the suspended mass will be [CBSE PMT 1990; Pb. PET 2002]
A.	\[T=2\pi \sqrt{\left( \frac{m}{{{K}_{1}}+{{K}_{2}}} \right)}\]
B.	\[T=2\pi \sqrt{\left( \frac{m}{{{K}_{1}}+{{K}_{2}}} \right)}\]
C.	\[T=2\pi \sqrt{\left( \frac{m({{K}_{1}}+{{K}_{2}})}{{{K}_{1}}{{K}_{2}}} \right)}\]
D.	\[T=2\pi \sqrt{\left( \frac{m{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)}\]
Answer» D. \[T=2\pi \sqrt{\left( \frac{m{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)}\]