Calculating Pendulum Angle and Amplitude: Homework Question and Equations

  • Thread starter Thread starter michaeltozer13
  • Start date Start date
  • Tags Tags
    Angle Pendulum
Click For Summary
SUMMARY

The discussion focuses on calculating the angular frequency and amplitude of a pendulum's motion based on a provided graph. The angular frequency is defined by the equation ω = √(g/L), where g represents gravitational acceleration and L is the length of the pendulum. Participants determined the period of the pendulum to be 6 seconds and the amplitude to be 1 degree. The conversation emphasizes the importance of understanding the relationship between angular frequency and period to solve for the pendulum's length.

PREREQUISITES
  • Understanding of pendulum motion and its equations
  • Knowledge of angular frequency and its calculation
  • Familiarity with the relationship between period and frequency
  • Basic grasp of gravitational acceleration (g)
NEXT STEPS
  • Learn how to derive the length of a pendulum using angular frequency
  • Study the concept of amplitude in simple harmonic motion
  • Explore the differences between angular frequency and frequency in Hertz
  • Investigate the effects of varying gravitational acceleration on pendulum motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify pendulum dynamics.

michaeltozer13
Messages
5
Reaction score
0

Homework Statement


a)The angle that the string of a long pendulum makes with the vertical is shown as a function of time. What is the angular frequency of the pendulum?
b)What is the amplitude of the pendulum's motion, in meters?

Homework Equations


Angular frequency=sqrt(g/L)

The Attempt at a Solution


im trying to find the length of the pendulum from the graph provided but I am not sure how to do that..
By looking at the graph i think the period is 6 seconds,and the amplitude is 1deg.. but I am not sure how to proceed from here. Any advice would be helpful, Thanks!
 

Attachments

  • Screenshot (12).png
    Screenshot (12).png
    63.3 KB · Views: 737
Physics news on Phys.org
Do you know the definition of angular frequency? Do you know how frequency is related to the period? Do you know how to manipulate the frequency expression you gave to solve for L?
 
Yes, Dr. D is correct up there. Think what the definition of angular frequency is Warning: angular frequency is a bit different from frequency in Hertz you get from graphs as the number of full wavelengths per second.

You already know the relationship between angular frequency and length of the string. (## \omega = \sqrt{\frac{g}{l}} ##)

Now you only have to determine angular frequency from the period that you determined from the graph. Good luck! ^^
 

Similar threads

Foucault Pendulum at the North Pole
  • · Replies 9 ·
Replies
9
Views
2K
Differential Equation of a Pendulum
  • · Replies 32 ·
2
Replies
32
Views
2K
Seeking advice on "simple" pendulum problem
  • · Replies 27 ·
Replies
27
Views
2K
Simulating a Rotary Inverted Pendulum in Python
  • · Replies 15 ·
Replies
15
Views
2K
Work done on a conical pendulum
  • · Replies 3 ·
Replies
3
Views
2K
Difference between maximizing amplitude by choosing omega_0 given omega_d versus choosing omega_d given omega_0.
  • · Replies 4 ·
Replies
4
Views
1K
Tension in the string of a simple pendulum
  • · Replies 4 ·
Replies
4
Views
3K
Equation Demonstration -- Simple Pendulum Analysis
  • · Replies 5 ·
Replies
5
Views
2K
For a Pendulum: Knowing Acceleration Find Maximum Angle
  • · Replies 26 ·
Replies
26
Views
3K
Max Impulse on a pendulum
  • · Replies 1 ·
Replies
1
Views
960