Relating y=mx+c and T^2=kd^3+4pi^2l/g

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SUMMARY

The discussion centers on the relationship between the linear equation y=mx+c and the equation T^2=kd^3+4π²l/g, which describes the period of a pendulum. The first equation represents a straight line in two-dimensional space, while the second is derived from experimental observations in pendulum motion, where T is the period, d is the distance, k is a constant, and g is the acceleration due to gravity. Participants express confusion regarding the connection between these two equations, emphasizing the need for context in understanding their relationship.

PREREQUISITES
  • Understanding of linear equations, specifically y=mx+c
  • Familiarity with pendulum motion and the formula T^2=kd^3+4π²l/g
  • Basic knowledge of constants in physics, such as k and g
  • Ability to interpret experimental data related to pendulum dynamics
NEXT STEPS
  • Research the derivation of the equation T^2=kd^3+4π²l/g in the context of pendulum motion
  • Study the principles of simple harmonic motion (SHM) and its mathematical representations
  • Explore the significance of the constant k in various physical equations
  • Investigate the effects of gravitational acceleration (g) on pendulum behavior
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and pendulum dynamics, as well as educators seeking to clarify the relationship between linear equations and physical motion equations.

Natalie Morris
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Homework Statement


Can someone please tell me how these two equations are related

Homework Equations


y=mx+c; T^2=kd^3+4pi^2l/g[/B]
 
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The first is just the generic equation for a line in 2-D space. The second does not seem to be related to it at all. Are we supposed to just guess where you got these and why you want to compare them? That is, should we just guess what the context of your question is?
 
Natalie Morris said:

Homework Statement


Can someone please tell me how these two equations are related

Homework Equations


y=mx+c; T^2=kd^3+4pi^2l/g[/B]
Hi NM. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

I don't recognize the kd^3 term. Where did this equation for T^2 come from?

This old thread may hold some answers: https://www.physicsforums.com/threads/shm-pendulum-length-gravity-question.529318/
 
Last edited by a moderator:
Well we got a pendulum lab to perform and had to relate the period T^2 to the distance of a yielding support d^3. That equation was provided to us to use to determine the values of k and g in the equation, where k was a constant and g was acceleration of free fall
 

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