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 $10cm$. Find the period of small vertical oscillations of $P$ about its equilibrium position. (use $g=9.8m/s^2$).

Answer 1

Unstretched length of the spring

$l_0=25mm$

Length of the upper spring

$l_1=20cm$

Length ofthe bottom spring

$l_2=10cm$

Find time period$=?$

$T=\frac{1}{2\pi }\sqrt{\frac{l}{g}}=\frac{1}{2\pi }\sqrt{\frac{20}{10}}=\frac{\sqrt{2}}{2\pi }=\frac{1}{\sqrt{2}\pi }s$