Mechanics Problem: Time Period of Simple Pendulum with Uniform Rod and Mass m

  • Thread starter Thread starter neelakash
  • Start date Start date
  • Tags Tags
    Mechanics
neelakash
Messages
491
Reaction score
1

Homework Statement



In a simple pendulum the string supporting the bob is replaced by a uniform rod of length L and mass M.Find the nw time period for small oscillations.Mass of the bob m.

Any help how to do it correctly?

Homework Equations


The Attempt at a Solution



Any help how to do it correctly?
 
Physics news on Phys.org
i guess the mass of string was neglected
and now since the rod has mass M, the CG of the system has changed
 
Basically, this is a physical pendulum now. Sure, the centre of mass has changed. So has the moment of inertia. If I remember right, the moment of inertia of a physical pendulum determines its period, but you'll have to derive the exact relation.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Number of quantum accessible states of a particle given T, N?'

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
View full post »

Similar threads

How Does a Variable Mass Affect a Simple Pendulum?
Replies
9
Views
3K
B Harmonic oscillator and simple pendulum time period
Replies
36
Views
3K
I Lagrangian for pendulum
Replies
11
Views
2K
Lagrange mechanics: Pendulum attached to a massless support
Replies
2
Views
4K
Oscillatory motion problem: Bicycle wheel rotation oscillation
Replies
17
Views
928
Derivation of time period for physical pendula without calculus
Replies
3
Views
2K
Experiment to determine the time period of a pendulum
Replies
12
Views
2K
What are the simple modes and frequencies for weakly coupled oscillators?
Replies
4
Views
2K
Two pendulums connected with a massless rope
Replies
3
Views
2K
The period of a simple pendulum
Replies
20
Views
2K

Hot Threads

Recent Insights

Back
Top