What Should the Expected Slope of T^2 vs. L and T^2 vs. M' Graphs Be?

  • Thread starter Thread starter brimister47
  • Start date Start date
  • Tags Tags
    Graphs
Click For Summary
SUMMARY

The expected slope of the T² vs. L graph in a pendulum experiment is defined by the equation T² = (4π²/g) x L, where g is the acceleration due to gravity. The calculated slope for T² vs. L is 3.223, while for T² vs. M', it is 3.616. The relationship for T² vs. M' can be derived from the equation T² = (4π²m)/k, indicating that the slope is (4π²)/k, where k is the spring constant. This discussion clarifies the calculations necessary to derive the gravity constant g from the slope of the T² vs. L graph.

PREREQUISITES
  • Understanding of pendulum mechanics and oscillation principles
  • Familiarity with the equations of motion for simple harmonic motion
  • Knowledge of graphing linear equations and interpreting slopes
  • Basic understanding of spring constants and mass in oscillatory systems
NEXT STEPS
  • Calculate the gravity constant g using the slope from the T² vs. L graph
  • Explore the relationship between mass and spring constant in oscillatory systems
  • Learn about the effects of varying mass on the period of a pendulum
  • Investigate the derivation of the formula T² = (4π²m)/k for oscillating springs
USEFUL FOR

Students conducting physics experiments, educators teaching mechanics, and anyone interested in the principles of oscillation and gravity calculations.

brimister47
Messages
5
Reaction score
0

Homework Statement


What is the expected slope of the line? What was the actual slope of the line of best fit? Calculate the gravity constant g from the slope of your graph

Homework Equations


k = (Mg) / (y_0 - y)

4pi^2/g x L = T^2

The Attempt at a Solution



I understand how to acquire gravity using the second equation for T^2 vs L. But I don't have a clue what my expected slope should be for either graph. My calculated slope for T^2 vs L is 3.223 and for T^2 vs. M' 3.616
 
Physics news on Phys.org
If you graph y vs x and the formula is y = mx,
then the slope is expected to be m.
If you graph T² vs L and the formula is T² = (4pi²/g) x L
then the expected slope is (4pi²/g). The calc for g would then be
g = 4pi²/slope

I don't see a formula relating T² and M'. What is M'?
It looks like you might be doing a pendulum experiment?
 
So that means my expected slope would be ~4? This was a pendulum experiment for T^2 vs L and and oscillating spring for T^2 vs M'. M' is the mass of our hook + spring + added weight, while M is just the mass of our weight added to the hook and spring.

Through my notes I found the equation T^2 = (4pi^2m)/k. So if I replace y=T^2 and x=m does that mean my slope is (4pi^2)/k?
 
Yes, that is the idea. Good luck.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
8K
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 2 ·
Replies
2
Views
13K
  • · Replies 10 ·
Replies
10
Views
8K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 13 ·
Replies
13
Views
3K