Question

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

• A. $T = 2 \pi \sqrt{ \frac{ m}{ k_1 - k_2 }} $
• B. $T = 2 \pi \sqrt{ \frac{ m k_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 ( k_1 + k_2)}{ k_1k_2 }} $

Answer 1

Answer: (D)

The effective spring constant of two springs in series is $k=\frac{k_{1} k_{2}}{k_{1}+k_{2}}$
Time period, $T=2 \pi \sqrt{\frac{m}{k}}=2 \pi \sqrt{\frac{m\left(k_{1}+k_{2}\right)}{k_{1} k_{2}}}$