Question

Two identical springs are attached to a small block $P$. The other ends of the springs are fixed at $A$ and $B$. When $P$ is in equilibrium the extension of top spring is $20cm$ and extension of bottom spring is $10cm$. The period of small vertical oscillations of $P$ about its equilibrium position is (use $g=$ $9.8m/s^2)$

• A. $\frac{2\pi }{7}sec$
• B. $\frac{\pi }{7}sec$
• C. $\frac{2\pi }{5}sec$
• D. none of these

Answer 1

Answer: (B)

$Mg=K\times 20-K\times 10\Rightarrow K=\frac{mg}{10/100}N/m$

$T=2\pi \sqrt{\frac{M}{K}}$
$T=2\pi \sqrt{\frac{1}{49\times 4}}=\frac{\pi }{7}sec$