Question

An object of unknown mass m is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has stretched by 14 cm. The object is then given a slight push upward and executes SHM. Determine the period T of this oscillation.

Answer 1

The period T of the SHM

$$T=2\pi\sqrt{\frac{m}{k}}$$

Since,

$$mg=k\Delta l$$

so

$$\frac{m}{k}=\frac{\Delta l}{g}$$

Finally

$$T=2\pi\sqrt{\frac{\Delta l}{g}}=6.28*\sqrt{\frac{0.14}{9.8}}=0.75\:\rm s$$