Question

A system is shown in the figure. The time period for small oscillations of the two blocks will be:


(correct answer + 2, wrong answer - 0.50)

• A. $2\pi \sqrt{\frac{3m}{k}}$
• B. $2\pi \sqrt{\frac{3m}{4k}}$
• C. $2\pi \sqrt{\frac{3m}{8k}}$
• D. $2\pi \sqrt{\frac{3m}{2k}}$

Answer 1

The correct option is B $2\pi \sqrt{\frac{3m}{4k}}$

Both the springs are in series.
$K_{eq}=\frac{k\left(2k\right)}{k+2k}=\frac{2k}{3}$
Time period $T=2\pi \sqrt{\frac{\mu }{k_{eq}}}$
Where $\mu =\frac{m_1{m}_2}{m_1+m_2}$
Here , $\mu =\frac{m}{2}$
$\therefore T=2\pi \sqrt{\frac{m}{2}.\frac{3}{2K}}=2\pi \sqrt{\frac{3m}{4k}}$