How Is Angular Frequency Calculated for a Plank Supported by a Spring?

Click For Summary
SUMMARY

The angular frequency of small oscillations for a uniform plank of mass 2.0 kg and length 1.0 m, pivoted at one end and supported by a spring with a spring constant (k) of 1000 N/m, is calculated to be 39 s-1. The moment of inertia (I) for the plank is determined using the formula I = (1/3) * M * (L2), where M is the mass and L is the length. The period (T) of oscillation is derived from the equation T = 2π√(I/mgr), where r is the distance from the center of mass. The frequency (f) is then obtained by taking the inverse of the period.

PREREQUISITES
  • Understanding of angular frequency and oscillations
  • Familiarity with the moment of inertia formula for a uniform rod
  • Knowledge of spring constants and Hooke's Law
  • Basic principles of rotational dynamics
NEXT STEPS
  • Study the derivation of angular frequency in oscillatory systems
  • Learn about the moment of inertia for various shapes and its applications
  • Explore the relationship between spring constants and oscillation frequency
  • Investigate the effects of pivot points on the dynamics of oscillating bodies
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of oscillating systems and spring mechanics.

kkred
Messages
1
Reaction score
0
A uniform plank of mass 2.0kg and length 1.0m is pivoted at one end
in a horizontal plane. It is supported at the other end by a spring with
k = 1000 N/m . What is the angular frequency of small oscillations? It m
may interest you to know that the moment of inertia of a uniform rod about its end is 1/3*M(L^2) where M is the mass and L is the length.


Tried to find Angular frequency by using angular momentum but I didn't find a suitable way to do it. Any suggestions?

The answer is 39s^-1
 
Physics news on Phys.org
use T=(2*3.14(I/mgr)^(1/2))
r is the distance from center of mass
Then inverse T to calculate the value of f.
 

Similar threads

Angular acceleration of plank hanging off edge with a weight
  • · Replies 7 ·
Replies
7
Views
2K
Angular frequency of plank attached to spring
  • · Replies 1 ·
Replies
1
Views
2K
How Do You Calculate the Natural Angular Frequency of a Dual-Spring System?
  • · Replies 5 ·
Replies
5
Views
4K
Sum of oscillating frequency and angular velocity
  • · Replies 11 ·
Replies
11
Views
2K
Find ω, the angular frequency of oscillation of the object
  • · Replies 4 ·
Replies
4
Views
2K
Simple Harmonic Motion and angular frequency
  • · Replies 1 ·
Replies
1
Views
3K
How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
  • · Replies 335 ·
12
Replies
335
Views
17K
Rotating simple harmonic oscillator
  • · Replies 11 ·
Replies
11
Views
2K
How to Calculate Amplitude Decrease in Damped Harmonic Motion After 10 Cycles?
  • · Replies 3 ·
Replies
3
Views
986
Find velocities when a mass leaves a system of a rod with two masses
  • · Replies 10 ·
Replies
10
Views
3K