Question

A mass ' $m$ 'is suspended from 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

• A. $T =2 \pi \sqrt{\frac{ m }{ k _{1}- k _{2}}}$
• B. $T =2 \pi \sqrt{\frac{ mk _{1}\, k _{2}}{ k _{1}+ k _{2}}}$
• C. $T =2 \pi \sqrt{\frac{ m }{ k _{1}+ k _{2}}}$
• D. $T =2 \pi \sqrt{\frac{ m \left( k _{1}+ k _{2}\right)}{ k _{1} k _{2}}}$

Answer 1

Answer: (D)

$K_{e q}=\frac{k_{1} \,k_{2}}{k_{1}+k_{2}}$
$T=2 \pi \sqrt{\frac{m}{k_{e q}}}$