Question

Two springs are joined and attached to a mass of $16\, kg$. The system is then suspended vertically from a rigid support. The spring constant of the two springs are $ {{k}_{1}} $ and $ {{k}_{2}} $ respectively. The period of vertical oscillations of the system will be

• A. $ \frac{1}{8\pi }\sqrt{{{k}_{1}}+{{k}_{2}}} $
• B. $ 8\pi \sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}}} $
• C. $ \frac{\pi }{2}\sqrt{{{k}_{1}}-{{k}_{2}}} $
• D. $ \frac{\pi }{2}\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}} $

Answer 1

Answer: (B)

The two springs are in series. Therefore, the time period is
$T=2 \pi \sqrt{\frac{m}{k}}=2 \pi \sqrt{m\left(\frac{k_{1}+k_{2}}{k_{1} k_{2}}\right)}$
As $m=16\, kg ; T=8 \pi \sqrt{\frac{k_{1}+k_{2}}{k_{1} k_{2}}}$