Period for harmonic motion (horizontal)

Click For Summary
SUMMARY

The discussion focuses on the relationship between the period of harmonic motion and the parameters of a cantilever beam setup, specifically a light flexible rod with a length "x" hanging freely from a horizontal table. The key equation to determine the period T of the end of the rod, which is influenced by the length "x" and the mass at the end, is derived from principles of cantilever dynamics. Participants referenced the concept of "cantilever with end mass frequency" to explore the mathematical relationships involved.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with cantilever beam theory
  • Basic knowledge of mass-spring systems
  • Ability to apply equations of motion in physics
NEXT STEPS
  • Research the equations governing cantilever beam dynamics
  • Study the derivation of the period of a cantilever with an end mass
  • Explore the effects of varying mass on the frequency of oscillation
  • Learn about the applications of harmonic motion in engineering
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of flexible structures and harmonic motion analysis.

hms.tech
Messages
246
Reaction score
0
Consider a light flexible rod placed on a horizontle table with part of the rod (length say "x") hanging freely (ie without support of the table) see attachment for clarity

A mass is also hung from the rod t one end.

Are there any equations that relate the Period T of the end of the rod to the length "x" , and the mass(hanging) ?
 

Attachments

  • Untitled.png
    Untitled.png
    2.6 KB · Views: 515
Physics news on Phys.org
Look up "cantilever with end mass frequency".
 

Similar threads

High School Harmonic oscillator and simple pendulum time period
  • · Replies 36 ·
2
Replies
36
Views
4K
Undergrad Equation of motion for a simple mechanical system
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Tension of a rod rotating on a horizontal table about a vertical axis
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Help to model transmission of forces through a medium
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Is a Vertically Hung Spring Mass System SHM?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Alternative Approach to Solving Foucault's Pendulum Behavior
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad A problem with non evident first integral
  • · Replies 17 ·
Replies
17
Views
2K
How to prove that motion is periodic but not simple harmonic?
  • · Replies 51 ·
2
Replies
51
Views
4K
Undergrad Period of a mass spring system with 2 spring of same K(vert)
  • · Replies 1 ·
Replies
1
Views
2K
Challenge How do you calculate the motion of a ball rolling on a rotating table?
  • · Replies 62 ·
3
Replies
62
Views
10K