Calculating Pendulum Angle and Amplitude: Homework Question and Equations

In summary, the conversation revolves around finding the angular frequency and amplitude of a pendulum based on a provided graph. The equation for angular frequency is given as sqrt(g/L), and the period is determined to be 6 seconds. The participants discuss the definition of angular frequency and its relationship to the length of the pendulum string. Ultimately, the solution involves manipulating the equation to solve for the length with the known period.
  • #1
michaeltozer13
5
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!
 

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  • #2
Do you know the definiton 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?
 
  • #3
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! ^^
 

FAQ: Calculating Pendulum Angle and Amplitude: Homework Question and Equations

1. What is a pendulum angle?

A pendulum angle is the measure of the angle between the suspended pendulum and its starting position. It is typically measured in degrees or radians.

2. How does the length of a pendulum affect its angle?

The length of a pendulum directly affects its angle. The longer the pendulum, the smaller the angle it will swing at. The shorter the pendulum, the larger the angle it will swing at.

3. What factors can affect the pendulum angle?

The pendulum angle can be affected by various factors such as the length of the pendulum, the mass of the pendulum, air resistance, and the initial force given to the pendulum.

4. How is the pendulum angle related to the period of the pendulum?

The pendulum angle is directly related to the period of the pendulum. The period is the time it takes for the pendulum to complete one full swing. As the angle increases, the period also increases.

5. Can the pendulum angle be used to measure time?

Yes, the pendulum angle can be used to measure time. The period of a pendulum is constant, meaning that for a given length, the time it takes for one full swing will always be the same. This principle is the basis for pendulum clocks.

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