First slide

Applications of SHM

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 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/s²)

Moderate

A

$\frac{2 π}{7} \sec$
B

$\frac{π}{7} \sec$
C

$\frac{2 π}{5} \sec$
D

none of these

Solution

$\begin{array}{l} M g = k \times 20 - k \times 10 \\ \Rightarrow k = \frac{m g}{10 / 100} N / m \\ T = 2 π \sqrt{\frac{M}{k}} \\ = 2 π \sqrt{\frac{1}{49 \times 4}} = \frac{π}{7} \sec \end{array}$

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