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  4. 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 20 cm and extension of bottom spring is 10 cm. The period of small vertical oscillations of P about its equilibrium position is (use g= .9.8 m / s 2)

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Q. 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 $20 \,cm$ and extension of bottom spring is $10\, cm$. The period of small vertical oscillations of $P$ about its equilibrium position is (use $g=$ $\left.9.8\, m / s ^{2}\right)$Physics Question Image

Oscillations

Solution:

$M g=K \times 20-K \times 10 \Rightarrow K=\frac{m g}{10 / 100} N / m$
image
$T=2 \pi \sqrt{\frac{M}{K}}$
$T=2 \pi \sqrt{\frac{1}{49 \times 4}}=\frac{\pi}{7} sec$