Question

Find the time period of oscillation of the spring - mass system assuming strings, pulleys and springs are light.

• A. $2\pi \sqrt{\frac{11m}{5k}}$
• B. $2\pi \sqrt{\frac{7m}{9k}}$
• C. $2\pi \sqrt{\frac{5m}{6k}}$
• D. $2\pi \sqrt{\frac{10m}{3k}}$

Answer 1

The correct option is D $2\pi \sqrt{\frac{10m}{3k}}$

Time period of spring-mass system is given by , $T=2\pi \sqrt{\frac{m}{k}}$

From the diagram given in the question, all the springs connected are in series,

$\therefore T=2\pi \sqrt{m(\frac{1}{k}+\frac{1}{3k}+\frac{2}{k})}$

$\Rightarrow T=2\pi \sqrt{\frac{10m}{3k}}$

Hence, option $\left(d\right)$ is correct.