Spring constant and uncertainty in spring constant calculation

Click For Summary
SUMMARY

The calculation of the spring constant (k) and its uncertainty (σ_k) is determined using the formula k = [4(π)^2]/slope. The uncertainty in the spring constant is directly related to the uncertainty in the slope, as there are no uncertainties associated with the constants like π. The percentage uncertainty in the slope translates to the percentage uncertainty in k, allowing for a straightforward calculation of σ_k.

PREREQUISITES
  • Understanding of harmonic motion and oscillations
  • Familiarity with the concept of spring constant (k)
  • Knowledge of uncertainty propagation in measurements
  • Basic proficiency in using mathematical equations involving constants
NEXT STEPS
  • Study the principles of harmonic motion and how they relate to spring constants
  • Learn about uncertainty propagation techniques in physics
  • Explore the calculation of percentage uncertainty in measurements
  • Review the significance of constants in physical equations, particularly π
USEFUL FOR

Students in physics courses, particularly those studying mechanics, as well as educators and anyone involved in experimental physics who needs to calculate spring constants and their uncertainties.

vcooper28
Messages
1
Reaction score
0

Homework Statement



The spring constant (k) and uncertainty in the spring constant(sigma_k) have to be calculated with the values available for: period (T), number of oscillations (N), mass (m), time, slope and uncertainty in slope. The spring constant can be done with the first equation but I have no idea how to calculate the uncertainty in the spring constant.

Homework Equations


k=[4(pi)^2]/slope

[k+/- (sigma_k)] = [4(pi)^2]/[slope +/- (sigma_k)]


The Attempt at a Solution

 
Physics news on Phys.org
vcooper28 said:

Homework Statement



The spring constant (k) and uncertainty in the spring constant(sigma_k) have to be calculated with the values available for: period (T), number of oscillations (N), mass (m), time, slope and uncertainty in slope. The spring constant can be done with the first equation but I have no idea how to calculate the uncertainty in the spring constant.

Homework Equations


k=[4(pi)^2]/slope

[k+/- (sigma_k)] = [4(pi)^2]/[slope +/- (sigma_k)]

The Attempt at a Solution


The only uncertainty you have in k - given your formula - is the uncertainty in the slope.
There is no uncertainty in the constants like π, so you use the percentage uncertainty of the slope as the percentage uncertainty of k.
 

Similar threads

Replies
29
Views
3K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
5
Views
2K
Replies
17
Views
2K
Replies
10
Views
1K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
1K