Question

In the laboratory, you attach a 300g mass to a spring of negligible mass and let it start to oscillate. The elapsed time from when the mass first moves through the equilibrium position to the second time it moves through that point is 2s. Find the force constant of the spring.

Answer 1

Given:

$m=0.3\:\rm kg$

$\tau=2\:\rm s$

The period of oscillation

$$T=2\tau=2*2\:\rm s=4\:\rm s$$

Also

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

Hense, the force constant of the spring

$$k=\frac{4\pi^2m}{T^2}=\frac{4*3.14^2*0.3}{4^2}=0.74\:\rm N/m$$