What are the Normal Mode Frequencies for a Hanging Rod's Vertical Oscillation?

Click For Summary
SUMMARY

The discussion centers on determining the normal mode frequencies of a uniform rod oscillating vertically when suspended from a massless string. The rod's length is denoted as 'a', and the problem involves analyzing the system using two angles: one between the string and the vertical, and another between the string and the rod. Key steps include calculating the center of mass velocity (v(COM)) and deriving the total kinetic energy (T) based on the rod's angular velocity. The inquiry highlights the necessity of understanding the mass distribution and dynamics involved in the oscillation.

PREREQUISITES
  • Understanding of classical mechanics principles, specifically oscillations
  • Familiarity with angular velocity and center of mass concepts
  • Knowledge of kinetic energy calculations in dynamic systems
  • Experience with analyzing systems of rigid bodies
NEXT STEPS
  • Study the derivation of normal mode frequencies in oscillating systems
  • Learn about the dynamics of rigid body motion in classical mechanics
  • Explore the concept of center of mass and its implications in oscillations
  • Investigate the mathematical treatment of angular momentum in oscillatory systems
USEFUL FOR

Students and educators in physics, particularly those focusing on mechanics and oscillatory motion, as well as researchers interested in the dynamics of rigid bodies.

benij_chaos
Messages
3
Reaction score
0
I Have a question that is bugging me because I can't get the answer out here's the question:

A uniform rod of length a hangs vertically on the end of an inelastic string of length a, the string being attached to the upper end of the rod. What are the frequencies of the normal modes of oscillation in the vertical plane.

Any help would be appreciated thanks
 
Physics news on Phys.org
benij, it is required that you show your thoughts/efforts when asking for help with coursework/textbook problems.
 
I set the problem up with two angles, one that joins the string to the vertical and one that joins the string to the rod. My problem comes in not knowing how treat the mass in the question. I have tried dividing it up into two parts and that does not seem to work. I am effectively stuck before I am started.
 
Can you find the velocity of the center of mass of the rod, in terms of the lengths and angles (and their derivatives)? From v(COM) and the angular velocity about its top end, you can then write down the total kinetic energy term, T.

PS: I don't know what 2 masses you are talking about. The string is massless.
 
Last edited:

Similar threads

Normal modes of four coupled oscillating masses (Kleppner and Kolenkow)
  • · Replies 4 ·
Replies
4
Views
3K
Spring constant matrix and normal modes (4 springs and 3 masses)
  • · Replies 2 ·
Replies
2
Views
3K
To find the distance of a horizontally suspended rod from a ceiling
  • · Replies 2 ·
Replies
2
Views
1K
Sound of vibrating string - modes
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Error tolerant normal mode frequency
  • · Replies 7 ·
Replies
7
Views
2K
Equation of motion and normal modes of a coupled oscillator
  • · Replies 1 ·
Replies
1
Views
1K
How Do You Calculate Normal Modes in a Vertical Coupled Oscillator System?
  • · Replies 1 ·
Replies
1
Views
3K
Form of the displacement, y(x,t), for the normal modes of a string
  • · Replies 4 ·
Replies
4
Views
2K
Small oscillation frequency of rod and disk pendulum
  • · Replies 5 ·
Replies
5
Views
3K
What Is the Frequency of Small Oscillations for a Pivoted Rod with Two Springs?
  • · Replies 19 ·
Replies
19
Views
2K