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

AI Thread Summary
The discussion centers on determining the normal mode frequencies for a uniform rod hanging vertically from an inelastic string. The user is struggling with how to treat the mass of the rod and has attempted to divide it into two parts without success. They seek guidance on finding the velocity of the center of mass in relation to the lengths and angles involved. The user emphasizes the need to express the total kinetic energy term based on this velocity and angular velocity. Clarification is also requested regarding the mention of two masses, as the string is considered massless.
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:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

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

Hot Threads

Recent Insights

Back
Top