Amass of 0.30kg is attached to a spring and is set in motion with a period of 0.24 s. what is the spring constantof the spring

The spring constant of the spring is 205.42 N/m.

Explanation:

Springs have their own natural "spring constants" that define how stiff they are. The letter k is used for the spring constant, and it has the units N/m.

                                                          k = -F/x

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

Given:

mass of object in SHM = m = 0.30 kg

Time period of the spring mass system = 0.24s

Spring constant = k ?

Finding 'k' using Time period 'T':

We know that

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.