Finding g from a Compound Pendulum Graph

In summary, the compound pendulum experiment is to measure the period of oscillation of the pendulum by measuring how long it takes for it to make 10 oscillations. The method to find the acceleration due to gravity is not really making much sense.
  • #1
Motorbiker
34
1
Thread moved from the technical forums, so no HH Template is shown.
I am doing the compound pendulum experiment but I am stuck on how to find the value of g from the graph

Here's a description of the compound pendulum:

The compound pendulum AB is suspended by passing a knife edge through the first hole. The pendulum is pulled aside through a small angle and released, whereupon it oscillates in a vertical plane with a small amplitude. The time for 10 oscillations is measured. From this the period T of oscillation of the pendulum is determined.

The method to find the acceleration due to gravity, is not really making much sense.

Please see it below:

A graph is drawn with the distance d of the various holes a straight line is drawn parallel to the X- axis from a given period T on the Y- axis, cutting the graph at four points A, B, C, D. The distances AC and BD, determined from the graph, are equal to the corresponding length l. The average length l = (AC+BD)/2. In a similar way , l/T2 is calculated for different periods by drawing lines parallel to the X-axis from the corresponding values of T along the Y- axis. l/T2 should be constant over all periods T, so the average over all suspension points is taken. the acceleration due to gravity is calculated from the equation g= 4π2(l/T2).

I don't know what the given period is, do you just use any random period? For I/T2, do you just like draw vertical lines parallel to all the values of T and then average the T values?
 
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  • #2
This would so be so much easier to understand with a sketch of the setup and a picture of the graph.
 
  • #3
I won't be able to upload a sketch of the setup since my printer isn't working at the moment.

Is it okay if I show you an accurate picture of the experiment and a picture of the graph? :smile:
 
  • #4
Motorbiker said:
Is it okay if I show you an accurate picture of the experiment and a picture of the graph?
That's a good start! :smile:
 

Related to Finding g from a Compound Pendulum Graph

1. What is a compound pendulum?

A compound pendulum is a physical system that consists of a rigid body suspended from a fixed point, allowing it to swing back and forth. It differs from a simple pendulum in that the rigid body has its own moment of inertia, which affects its motion.

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

The period of a compound pendulum is directly proportional to its length. This means that as the length increases, so does the period of oscillation. This can be seen in the equation T = 2π√(I/mgd) where T is the period, I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance from the pivot point to the center of mass.

3. What factors affect the period of a compound pendulum?

Aside from the length of the pendulum, other factors that affect the period include the mass of the rigid body, the distance of the center of mass from the pivot point, and the gravitational acceleration. Air resistance and friction may also play a role in affecting the period.

4. How is the period of a compound pendulum measured?

The period of a compound pendulum can be measured by recording the time for a certain number of oscillations and then dividing by the number of oscillations. This can be repeated multiple times to get an average value and reduce errors. Alternatively, the period can also be calculated using the equation T = 2π√(I/mgd) if the necessary values are known.

5. What are some real-world applications of compound pendulums?

Compound pendulums have many practical applications, such as in clock mechanisms, seismometers for measuring earthquakes, and suspension systems in vehicles. They are also used in experiments to study the effects of gravity and other physical forces on a system.

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