We are given information:
m = 80g = 0.080kg
x = 10cm = 0.10m
F = 0.2N
d = 20cm = 0.20m
This mass-spring system can be represented as harmonic oscilator. Harmonic oscilator is a type of oscilator where mass oscilates around equilibrium point. Maximum distance on both sides of equilibrium point remains same Period of oscilation is constant. In harmonic oscilator all outside forces are neglected.
In this problem we have mass attached to a spring so we can use spring formula:
F = -kx
where k = spring constant
We can rearrange this formula in order to calculate k. We will ignore negative sign.
k = F / x
k = 0.2 / 0.1
k = 2 N/m
Now we can use this information to calculate the period. Formula is:
[tex]T=2 \pi \sqrt{ \frac{m}{k} } \\ \\ T=2 \pi \sqrt{ \frac{0.080}{2} } \\ \\ T=1.26s[/tex]
We can see from formula that the period does not depend on maximum distance from equilibrium point. It only depends on mass and spring constant.
