Question

An object of weight 120N vibrates with a period of 4.0s when hang from a spring. Calculate the force per unit length of the spring [g=10m/s, π=3.142]

Answer 1

The period of oscillating spring is

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

or

$$T=2\pi \sqrt{\frac{P}{kg}}$$

From this we have force per unit length

$$k=\frac{4\pi^2P}{T^2g}$$

Calculating

$$k=\frac{4\cdot (3.142)^2\cdot 120}{10\cdot 4^2}=29.6 (\frac{N}{m})$$