Simple harmonic oscillation: uniform rod

In summary, the period of oscillations for a freely pivoted uniform rod of mass m and length L is 2π √2L/3g, with the distance between the center of mass and the end being L/2. This can be found using the equation for moment of inertia and solving for ω and T.
  • #1
vetgirl1990
85
3

Homework Statement


A uniform rod of mass m and length L is freely pivoted at one end. What is the period of its oscillations? Icm for a uniform rod rotating about its centre of mass is 1/12mL2

(a) √3g/2L
(b) 2π √3L/2g
(c) 2π √2L/3g
(d) 2π √L/g
(e) none of the above

Homework Equations


ω2 = mgL/I

Icm = 1/12mL2
I = Icm +1/12mL2

Period: T = 2π/ω

The Attempt at a Solution


I'm fairly certain that the answer is "none of the above", but I'd just like to make sure I'm not neglecting anything in what seems to be a simple plug-and-chug question.

I = Icm +1/12mL2 = 1/12mL2 + mL2 = 13/12 mL2

ω = √mgL/I= √(mgL)/(13/12)mL2 = √12g/13L

T = 2π/ω = 2π √13L/12g
 
Last edited:
Physics news on Phys.org
  • #2
What is the distance between the Centre of mass of rod and the end? Answer this and you'll realize what you did wrong.
 
  • Like
Likes vetgirl1990
  • #3
AbhinavJ said:
What is the distance between the Centre of mass of rod and the end? Answer this and you'll realize what you did wrong.
I just realized what I did wrong. The distance is L/2, so the moment of inertia equation turns into: I = 1/3mL2

So then ω2 = mg(L/2) / (1/3)mL2

Therefore T = 2π √2L/3g

Thanks!
 
  • #4
vetgirl1990 said:
Thanks!
Welcome :)
 

FAQ: Simple harmonic oscillation: uniform rod

What is simple harmonic oscillation?

Simple harmonic oscillation is a type of periodic motion in which an object moves back and forth around an equilibrium point, with a restoring force that is directly proportional to the displacement from the equilibrium point.

How does a uniform rod exhibit simple harmonic oscillation?

A uniform rod can exhibit simple harmonic oscillation when it is suspended from one end and allowed to swing freely. The weight of the rod creates a restoring force that causes it to oscillate back and forth.

What factors affect the period of a uniform rod's oscillation?

The period of a uniform rod's oscillation is affected by its length, mass, and the strength of the gravitational force acting on it. A longer rod will have a longer period, while a heavier rod or a rod in a stronger gravitational field will have a shorter period.

Can the amplitude of a uniform rod's oscillation be changed?

Yes, the amplitude of a uniform rod's oscillation can be changed by adjusting the initial displacement or the amount of energy given to the rod. The amplitude will also decrease over time due to the effects of friction and air resistance.

What are some real-life examples of simple harmonic oscillation?

Some common examples of simple harmonic oscillation include a pendulum, a mass on a spring, and a swinging door. In nature, simple harmonic motion can also be seen in the motion of planets and stars in orbit.

Similar threads

Replies
11
Views
618
Replies
1
Views
5K
Replies
25
Views
6K
Replies
5
Views
1K
Back
Top