A spring of spring constant k=12.5N/m is hung vertically. a 0.500kg mass is then suspended from the spring. what is the displacement of the end of the spring due to the wieght of the 0.500 kg mass?

The displacement of one end of the spring due to weight = 0.4 m.

Explanation:

Given :

Spring constant

Mass

From the hooke's law,

Force is proportional to the negative of the displacement.

  ∝

Where minus sign represent that, the force is always directed toward mean position.

Now one force is gravity acts as a downward. so we write,

Here we take only magnitude.

Where displacement of one end of spring,

    m

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.